Uses of systems with degrees of freedom poised between fully quantum and fully classical states

ABSTRACT

Disclosed herein are systems and uses of systems operating between fully quantum coherent and fully classical states. Such systems operate in what is termed the “Poised realm” and exhibit unique behaviors that can be applied to a number of useful applications. Non-limiting examples include drug discovery, computers, and artificial intelligence

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. application Ser. No.14/500,901, filed Sep. 29, 2014, which is a divisional of U.S.application Ser. No. 13/187,257, filed Jul. 20, 2011, which claims thebenefit of U.S. Provisional Application Nos. 61/367,781, filed Jul. 26,2010; 61/367,779, filed Jul. 26, 2010; 61/416,723, filed Nov. 23, 2010;61/420,720, filed Dec. 7, 2010; and 61/431,420, filed Jan. 10, 2011, allof which are incorporated herein by reference in their entirety.

BACKGROUND Field of the Invention

The present invention relates to systems and uses of systems operatingbetween fully quantum coherent and fully classical states. Non-limitingapplications include drug discovery, computers, and artificialintelligence.

Background Description

Many physical systems having quantum degrees of freedom quickly decohereto classicity for all practical purposes. Thus, many designed systemsconsider only classical behaviors. One example is in the field of drugdiscovery where traditional approaches to drug design considers thelock-and-key fitting of a molecule into an enzyme or receptor. Otherdesigned systems are carefully setup to maintain full quantum coherence,for example, the qubits in a quantum computer. However, recentdiscoveries have indicated several systems in nature that haverelatively slow decoherence. Birds are able to see magnetic field linesdue to a quantum coherent chemical reaction in their retina. Lightharvesting molecules are able to maintain quantum coherent electrontransport for times much longer than the expected coherence time at roomtemperatures. The existence of such cases demonstrates that quantumcoherence can exist at room temperature and at the presence of waterbath and evolution can ‘design’ quantum coherent structures to playcertain biological roles. Thus, there is a need for new systems thatutilize the unique properties that exist between full quantum coherenceand classicity.

SUMMARY OF THE INVENTION

Disclosed herein are various methods of classifying the state of asystem, such as a molecule interacting with its environment, in terms ofits degree of order, its degree of coherence, and/or its rate ofcoherence decay. Some embodiments include classifying only a single oneof these variables whereas other embodiments include classifying two orall three of the variables. These methods include classifying the systemin the course of creating systems that exist and/or operate at aspecific point or region of a classification space described thevariables discussed above and all practical outcomes of such creation.

Disclosed herein is a quantum reservoir computer that includes aplurality of nodes, each node comprising at least one quantum degree offreedom that is coupled to at least one quantum degree of freedom ineach other node; at least one input signal generator configured toproduce at least one time-varying input signal that couples to thequantum degree of freedom; and a detector configured to receive aplurality of time-varying output signals that couple to the quantumdegree of freedom.

Also disclosed herein is a method of drug discovery that includesselecting a biological target; screening a library of candidatemolecules to identify a first subset of candidate molecules that bind tothe biological target; determining the energy level spacing distributionof a quantum degree of freedom in each of the candidate molecules in thefirst subset; comparing the energy level spacing distribution to atleast one pre-determined reference function; and selecting a secondsubset of molecules from the first subset as drug candidates based onthe comparison.

Further disclosed herein is a method of drug discovery that includesselecting a biological target; screening a library of candidatemolecules to identify a first subset of candidate molecules that bind tothe biological target; determining the energy level spacing distributionof a quantum degree of freedom in each of the candidate molecules in thefirst subset; conducting an in vitro or in vivo assay for biologicalactivity on each of the candidate molecules in the first subset;correlating the energy level spacing distribution with activitydetermined from the in vitro or in vivo assay; determining the energylevel spacing distributions of a quantum degree of freedom in a new setof candidate molecules; comparing the energy level spacing distributionsof the new set of candidate molecules with energy level spacingdistributions that correlate with biological activity; and select asdrug candidates from the new set of candidate molecules those moleculeswhose energy level spacing distributions exhibit a pre-determined levelof similarity to the energy level spacing distributions that correlatewith biological activity.

Further disclosed herein is a method of drug discovery that includesselecting a biological target; screening a library of candidatemolecules to identify a first subset of candidate molecules that bind tothe biological target; measuring decoherence decay of a quantum degreeof freedom in each of the candidate molecules in the first subset;comparing the decoherence decay to at least one pre-determined referencefunction; and selecting a second subset of molecules from the firstsubset as drug candidates based on the comparison.

Further disclosed herein is a method of drug discovery that includesselecting a biological target; screening a library of candidatemolecules to identify a first subset of candidate molecules that bind tothe biological target; measuring decoherence decay of a quantum degreeof freedom in each of the candidate molecules in the first subset;conducting an in vitro or in vivo assay for biological activity on eachof the candidate molecules in the first subset; correlating thedecoherence decay with activity determined from the in vitro or in vivoassay; measuring decoherence decay of a quantum degree of freedom in anew set of candidate molecules; comparing the decoherence decay of thenew set of candidate molecules with the decoherence decay that correlatewith biological activity; and select as drug candidates from the new setof candidate molecules those molecules whose decoherence decay exhibit apre-determined level of similarity to the decoherence decay thatcorrelate with biological activity.

Further disclosed herein is a Trans-Turing machine that includes aplurality of nodes, each node comprising at least one quantum degree offreedom that is coupled to at least one quantum degree of freedom inanother node and at least one classical degree of freedom that iscoupled to at least one classical degree of freedom in another node,wherein the nodes are configured such that the quantum degrees offreedom decohere to classicity and thereby alter the classical degreesof freedom, which then alter the decoherence rate of remaining quantumdegrees of freedom; at least one input signal generator configured toproduce an input signal that recoheres classical degrees of freedom toquantum degrees of freedom; and a detector configured to receive quantumor classical output signals from the nodes.

Further disclosed herein a method of measuring the state of a physicalsystem that includes determining the degree of quantum coherence of atleast one degree of freedom in the system; determining the degree oforder of the system; and classifying the system based on the determineddegree of quantum coherence and the determined degree of order.

In one embodiment, determining the degree of order comprises measuringdecoherence decay of a quantum degree of freedom in the system. In oneembodiment, determining the degree of order comprises determining theenergy level spacing distribution of a quantum degree of freedom in thesystem. In one embodiment, the system is a molecule.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is graph depicting the boundaries of the Poised Realm.

FIG. 2 is a graph depicting an Erdos-Renyi Random Graph with GiantComponent.

FIG. 3 is a graph depicting the energy level spacing for Erdos-Renyirandom graphs.

FIG. 4 is a flowchart illustrating a drug discovery method.

FIG. 5 is a flowchart illustrating another drug discovery method.

FIG. 6 is a graph depicting the Giant Component of a 100 nodeErdos-Renyi Critical Random Graph.

FIG. 7 is a graph depicting the Giant Component of a 50 node Erdos-RenyiCritical Random Graph.

FIG. 8 is a block diagram of a computer utilizing quantum nodes andtime-varying inputs and outputs.

FIG. 9 is flowchart illustrating a training method for the computerdescribed in FIG. 8.

FIG. 10 is diagram of a liposome containing chromophores.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

Described herein are several new systems and uses of systems operatingin what is termed herein as the “Poised Realm.” By “Poised Realm,” it ismeant a physical system that does not exhibit fully quantum behavior norexhibits fully classical behavior. In this sense, the system is“poised”, or even can “hover” between the quantum and classical worlds.By Poised Realm, we mean any physical means or procedure to achieve sucha system poised between quantum and classical behavior, including asbounding limits, fully quantum coherent behavior and fully classicalbehavior.

In one characterization of the Poised Realm, we use two independentfeatures of, without loss of generality, open quantum systems. Thedegree of decoherence and/or recoherence is one feature. In addition totheir quantum, decohering, recohering, or classical behavior, physicalsystems may also be classified according to the degree of order orchaotic behavior that they exhibit along an order-criticality-chaosspectrum. Systems within the Poised Realm may be characterized by anydegree of order along this spectrum. In some embodiments, the physicalsystems described herein do not exhibit full order or chaos and are thusalso “poised” between order and chaos. Below we describe new theoremswhich establish that WITHIN the poised realm itself, ie not classical,critical poised realm systems in the presence of decoherence losecoherence most slowly, that is in a power law fashion, while ordered orchaotic Poised Realm systems lose coherence exponentially, hencedecohere much faster in the absence of recoherence.

As used herein, “recoherence” refers to a system entering again into asuperposition state after it once lost its coherence. The term“recoherence” commonly refers to the re-emergence of some initialquantum state during coherent quantum evolution, which is different fromthe meaning used herein.

Thus in at least one characterization of the Poised Realm, the PoisedRealm may be illustrated by a two-dimensional coordinate system havingas its y-axis (the vertical) the degree of quantum behavior, stretchingfrom fully quantum behavior at the “origin” to fully classical behavior“up” the y axis, typically by decoherence and movement down the Y axistoward quantum behavior via recoherence, and on the x-axis (thehorizontal) the degree of order, stretching from full order to fullchaos (see FIG. 1). The area on the graph between fully quantum andfully classical behavior is at least one definition of the “PoisedRealm.” The y axis in FIG. 1 can be infinite in that classical behaviorin some circumstances, in particular via increasing quantum decoherence,can be approached as closely as wished, i.e., achieved “For AllPractical Purposes” (FAPP).

Thus, as used herein, a “fully classical” system or a system that is“classical for all practical purposes” is a probabilistic mixture ofsingle amplitudes. A “fully quantum” system is one in which all or atleast one of quantum degrees of freedom comprise a superposition ofpossibility waves. Other possibilities or amplitudes may have lostsuperposition and be comprised by one “pure state” amplitude or a set ofpure state amplitudes called a “mixed state”. These terms may beunderstood by the classical double slit experiment, where photons incoherent fully quantum states exhibit an interference pattern. If adetector is used at one or more of the slits, interaction with thedetector causes the photons' wave functions to collapse such that theyare no longer quantum coherent (i.e., they exhibit classical behavior),resulting in loss of the interference pattern.

Degree of Order

The system in general can be described by its Hamiltonian H. Classicaltrajectories of the system can be calculated from the Hamiltonian viasolving its Hamiltonian equations. Quantization of the Hamiltonianresults in the Hamiltonian operator Ĥ, which fully describes thesystem's quantum dynamics via the Schrodinger equation. The Hamiltonianmay depend on several parameters of the system. By changing theparameters of the system we can change the form of its Hamiltonian.Later we refer to this as “changing the Hamiltonian”.

By changing the Hamiltonian we can change the degree of chaos in thesystem. Degree of chaos of trajectories can be characterized by theirLyapunov exponents. One can assign a Lyapunov exponent to each point inthe phase space by calculating the Lyapunov exponent of the trajectoryinitiated in the point. In the phase space one can find connected areaswhere the Lyapunov exponent is positive and characterized by the samevalue within the patch. These chaotic patches are separated by regularareas, where the Lyapunov exponent is zero. The degree of chaos in thesystem can be characterized by the relative proportion of the volume ofthe chaotic areas in the phase space. If no chaos is present, theproportion is zero. If the system is chaotic for almost all initialconditions the proportion is 1. The position of the system on the x-axis(the horizontal) is this ratio. Usually changing a parameter of theHamiltonian such a way that its Hamiltonian equations become morenonlinear increases the degree of chaos and moves the system to theright on the x-axis.

In the process of moving the system to the right on the x-axis newchaotic areas emerge, the size of the existing areas increase andseparation of some of the existing chaotic areas disappear. There is acritical point on the x-axis, x_(c), below which the chaotic areas formseparated patches in the phase space. Above the critical point thechaotic areas coalesce and form a giant connected component. Below thecritical point chaotic trajectories are confined within their chaoticarea in the phase space. Above the critical point chaotic trajectoriescan diffuse globally in the phase space.

In the critical point the Lyapunov exponent for the globally connectedchaotic area is zero and it goes through a second order phase transitionin the neighborhood of the critical point. It is zero λ₀(x_(c))=0 belowthe critical point x<x_(c) and shows power law scalingλ₀(x)˜(x−x_(c))^(β) above x>x_(c) with some positive exponent β.

Some quantum systems, such as spin systems are defined only with theirHamilton operator and their classical Hamiltonian cannot be defined. Insuch systems the x-axis and its critical point can be defined purelyquantum mechanically. In the pure ordered regime the phase space motionhappens on a torus. Quantum mechanically it is a separable system andits eigenenergies correspond to the quantization of its tori. The energyeigenvalues of the system follow Poissonian distribution. The nearestneighbor level spacing distribution is exponential:

p _(p)(s)=exp(−s)

where s_(n)=(E_(n+1)−E_(n))/Δ(E_(n)) is the level spacing measured inthe units of local mean level spacing Δ(E) at energy E. In the purelychaotic system the energy level statistics of the system can bedescribed by Random Matrix Theory (RMT) and the level spacing followsapproximately the Wigner surmise:

${p_{w}(s)} = {\frac{\pi \; s}{2}{\exp \left( {{- \pi}\; s^{2}\text{/}4} \right)}}$

These limiting cases correspond to the values 0 and 1 on the x-axisrespectively. In an intermediate situation, where the system is neitherfully ordered or fully chaotic, the quantity

$x = \frac{A - A_{p}}{A_{w} - A_{p}}$

can serve as the x-coordinate where

A_(p) = ∫₂^(∞)p_(p)(s), A_(w) = ∫₂^(∞)p_(w)(s),

and the quantity A is calculated from the actual level spacing of thesystem

A = ∫₂^(∞)p(s).

In the above mentioned quantum systems the criticality can be defined ina purely quantum mechanical way. In the ordered region theeigenfunctions of the Hamilton operator are localized in configurationspace. In the chaotic region the eigenfunctions are delocalized andextended over the configuration space of the entire system. The criticalvalue x_(c) separates these two behaviors. The level spacing statisticsin the critical point can be well approximated by the semi-Poissoniandistribution p(s)=4s exp(−2s).

Systems in nature don't exist in full separation. They are coupled totheir environment. Coupling a low dimensional quantum system to aninfinite degree environment exert random forces on the system. Thesystem loses its quantum coherence as a result. The environment-systemcoupling can be described by the Hamilton operatorĤ=Ĥ_(s)+Ĥ_(e-s)+Ĥ_(e), where the Hamiltonian operators correspond to thesystem Ĥ_(s), to the environment-system coupling Ĥ_(e-s) and to theenvironment Ĥ_(e). The strength of the external forces causingdecoherence is measured by the variance of system-environment couplingaveraged over the states of the environment Γ²=

Ĥ_(e-s)

. The position of the system on the y-axis (the vertical) is the ratioof F and the average level spacing Δ(E) of the system Ĥ_(s).

Some embodiments include modulating or controlling the degree of orderof a physical system (i.e., moving along the x-axis of FIG. 1). Somesuch embodiments include engineering a system to have a desired degreeof order. In various embodiments, the following describes, withoutlimitation, three methods for controlling the degree of order in asystem.

1) Position on the X-Axis Due to the Hamiltonian of a System.

In general, altering the Hamiltonian of the system by any means mayalter its position on the x axis. More specifically, due to the dynamicsof the Poised Realm system ITSELF, the classical Hamiltonian of thesystem can change, changing its position on the x-axis statically or, aswe will see, dynamically, as one non-limiting example, from order tocriticality to chaos and back.

Classical dynamical systems are often describable as flows on aHamiltonian. Such flows can, for example, and without limitation,describe most classical physical dynamical systems. A periodic pendulumis a simple example of a system in the ordered classical regimedescribable by a Hamiltonian. Analogous quantum oscillators are also inthe ordered regime. Other Hamiltonians can be critical or chaoticclassically.

The dynamical behaviors of such classical systems can be ordered on thex-axis from ordered to critical to chaotic, by means of diverse measuresof their dynamical behavior. Several such methods are known in the art.Without limitation, a preferred method to array classical Hamiltoniandynamical systems on the x-axis is by measuring their average Lyapunovexponent, as is known in the art, averaged over the time behavior forshort times and from multiple initial states of the system in question.The Lyapunov exponent measures whether nearby trajectories diverge,(chaos), converge, (order), or flow parallel to one another,(criticality), in state space. Account can be taken of the attractorbasin sizes, should the classical system have both at least oneattractor and may have more than one attractor, each “draining a basinof attraction.” Then, typically one measures the Lyapunov exponent oneach attractor and weights these by the basin sizes of that attractor,averaged over all attractors, to get a global measure of position on thex-axis. Alternatively, the Hamiltonian system may have no attractor, asin classical statistical mechanics and exhibit ergodic behavior, andsatisfy the Louiville equation, as is known in the art.

Thus, classical systems can be moved on the x-axis by “tuning” theirHamiltonians. As we will see, in the Poised Realm quantum degrees offreedom can become classical or classical for all practical purposes,FAPP, and thereby alter the classical Hamiltonian of the system, so thevery dynamics of Poised Realm systems can move the classical degrees offreedom from order to criticality to chaos and back.

2) Suppression of Decoherence.

Systems in the poised realm can be characterized by their position onthe x and y axes in terms of chaos-order and the strength of thecoupling to the environment. Depending on their position they areexposed to the decoherence caused by the environment. Quantum systemscan be described by their density matrices (ρ_(nm)) as it is known tothe art. Theoretically, the decay of coherence can be characterized bythe speed the off diagonal elements (n≠m) of the density matrix die outρ_(nm)˜^(e−t/t) ^(c) ; where τ_(c) is the coherence time. An overallmeasure of the speed of the loss of the coherence is the entropyproduction in the system. In practice the production of the standardShannon (S₁=−Tr[ρ log ρ]) entropy and the more easily computable Renyientropy (S₂=log Tr[ρ²]) are used.

The exponential time dependence of the off-diagonal elements of thedensity matrix and the entropy production rate are closely related:

$\frac{{dS}_{1\; {or}\; 2}}{dt} \sim \frac{1}{\tau_{c}}$

Entropy production due to decoherence is related to the dynamicalproperties of the system. It has been shown via semiclassical argumentsand direct simulations that after an initial transient the entropyproduction rate is related to the Kolmogorov-Sinai entropy (h_(KS)) ofthe dynamical system:

${\frac{{dS}_{1}}{dt} \sim h_{KS}} = {\sum\limits_{i}\lambda_{i}^{+}}$

which is in turn the sum of the positive Lyapunov exponents λ_(i) ⁺characterizing the exponential divergence of chaotic trajectories.Entropy production becomes slow when the largest Lyapunov exponent andthe Kolmogorov-Sinai entropy of a system vanishes (h_(KS)≠λ_(o)→0). Inthis case the coherence time becomes formally infinite T_(c)→∞indicating a slower than exponential decay of coherence in the system,where the off diagonal elements of the density matrix stay finite or dieout only in an algebraic way

${\rho_{nm}(t)} \sim \frac{1}{t^{\alpha}}$

where α is the exponent of the power law decay.

The zero entropy production state emerges in mechanical systems at theborder of the onset of global chaos x_(c) of the classical counterpartof the system. In quantum systems without classical counterpart thetransition happens also at x_(c), where x_(c) is now defined in terms ofthe critical level spacing p(s)=4s exp(−2s).

Suppose, we have a parameter ε of a mechanical system whichcharacterizes its transition from integrability to chaos:

H=H ₀ +εH ₁.

Here H₀ is the Hamiltonian of an integrable system. Classically andquantum mechanically it is a solvable system. Classically it can bedescribed by action-angle variables and it does only simple oscillationsin the angle variables. The phase space motion happens on a torus.Quantum mechanically it is a separable system and its eigenenergiescorrespond to the quantization of its tori. The energy eigenvalues ofthe system are random and follow a Poissonian distribution. The nearestneighbor level spacing distribution is exponential

p(s)=exp(−s);

where s_(n)=(E_(n+1)−E_(n))/Δ(E_(n)) is the level spacing measured inthe units of local mean level spacing Δ(E) at energy E. The HamiltonianH₁ is a perturbation. When ε≠0 the system is no longer integrableclassically and no longer separable quantum mechanically. At a givensmall ε, the Kolmogorov-Arnold-Moser (KAM) theory describes the system.The perturbation breaks up some of the tori in the phasespace andchaotic diffusion emerges localized between unbroken, so called KAMtori. Chaotic regions are localized in small patches in the phasespacesurrounded by regular parts represented by the KAM tori. At a givencritical ε KAM tori separating the system gets broken and the chaoticpatches merge into a single large chaotic sea. Above the transitionε>ε_(c), the system is fully chaotic characterized by a positive largestLyapunov exponent λ_(o)>0. The energy level statistics of the system canbe described by Random Matrix Theory (RMT) and the level spacing followsthe Wigner surmise:

${p(s)} = {\frac{\pi \; s}{2}{{\exp \left( {{- \pi}\mspace{11mu} s^{2}\text{/}4} \right)}.}}$

For our purposes the most important region is ε=ε_(c). In the transitionpoint the Lyapunov exponent is zero and it goes through a second orderphase transition in the neighborhood of the critical point. It is zeroλ_(o)(ε)=0 below the critical point ε<ε_(c) and shows power law scalingλ_(o)(ε)˜(ε−ε_(c))^(β) above ε>ε_(c) with some positive exponent. At thetransition point the level statistics is a special universal statisticscalled semi-Poissonian:

p(s)=4sexp(−2s).

In this transition point where entropy production is zero, the system isthe most robust against decoherence and a system can stay coherent foran anomalously long time in this point. Below the transition point thesystem is localized and no global transport is possible. Althoughentropy production is low in this region the system is not suitable forcomplex transport and also decoherence is strong as each separatelocalized patch in the phase-space supports a localized wave functionquantum mechanically. Each patch is affected by decoherence in a directway and coherence is lost exponentially rapidly. Far above thetransition point strong chaos induces mixing and entropy productionwhich causes rapid decoherence. Near the transition point from above,however metastable states are formed and the wave functions showcritical fractal structure. The complex geometry and spatial structureof these transitional states is able to avoid the effects of decoherencemost effectively.

The transition described above is much more general than just theintegrable-chaotic transition. An example is the metal-insulatortransition point. Such localization-global transport (conductance)transition is present when we add static random potential to a clean andperfectly conducting lattice. At a critical level of the added randompotential the system stops conducting and the system becomes insulatingdue to Anderson localization of its wave-function. In this system thecontrol parameter ε is the variance of the random potential. The energylevel statistics of the metallic system is described by RMT and thelocalized states produce Poissonian statistics. In the transition pointsemi-Poissonian statistics emerges. The same transition can occur alsoin the conducting properties of random networks (graphs). There thelocalization-global conductance transition occurs at the percolationthreshold, where the giant component of the network emerges. Finally,the same transition can be seen in finite quantum graphs by changing itsgeometry in specific ways.

In all these systems the metal-insulator critical point is characterizedby a fractal structure of the wave function similar to those in thechaos-integrability transition. Moreover, the equivalence of themetal-insulator and chaos-integrability transitions has also been provenanalytically. Therefore it seems reasonable to claim that thesuppression of the decoherence is also a universal feature of thecritical point of the metal-insulator transition. We can suppressdecoherence and keep our system coherent for an anomalously long time ifwe deliberately keep it in the transition point. We call this state thePoised Realm Critical.

Experimentally, the Poised Realm Critical state can be identified bymeasuring the decay of coherence in the system. In a non-critical systemthe coherence decay is exponential in time. The Poised Realm state issignaled by a slow, typically power law decay of coherence. State of theart coherence decay measurements are based on various echo measurementsdepending on the system studied. This includes spin echo, neuton spinecho, and photon echo.

3) Position on the X-Axis is Tunable by the Detailed and/or StatisticalStructure of Quantum Networks and Graphs.

As known in the art, quantum graphs and quantum networks may be used tomodel real systems such nano-structures. During dynamical behavior of aPoised Realm system, the structure of a quantum network corresponding toa real system can change, altering position on the x-axis.

It is convenient to start with the famous Erdos Renyi (ER) Random Graphsas the simplest possible examples of quantum networks. An ER graph is“grown” by starting with a set of N disconnected nodes. Random pairs ofnodes are chosen, and joined by a “line” or “link”. This process isiterated, so that at any point, some ratio of links/nodes exists. ERgraphs are extraordinary and have driven much research. Mostimportantly, they exhibit a first order phase transition fromessentially disconnected tree “subgraphs” to a single “Giant Component.”Define a “cluster” as a set of interconnected nodes. When the ratio oflinks/nodes is less than 0.5, the graph consists of isolated pieces. As0.5 is approached, initially small tree-like structures become largerand larger. At link/node ratio 0.5, when the number of ends of linksequals the number of nodes, the phase transition to a Giant Componentoccurs. Intuitively once there are a few very large tree-like graphs foran arc/node ratio a bit below 0.5, a few randomly connected nodes willtie all or most of the large tree-like nodes into the Giant Component(see FIG. 2).

Amazing things happen at this phase transition. Not only does the giantcomponent come to exist, but for the first time loops of all lengthsemerge in the giant component.

At the critical ratio of links/nodes, 0.5, the ER graph is said to be“critical”. But many nodes are still not connected.

As the ratio of links/nodes increases past 0.5 two major things happen.Isolated nodes and small trees are tied into an enlarging GiantComponent. Second, the Giant Component becomes increasingly richly crossconnected, so average <k> rises.

Such graphs can be considered static quantum networks. Their structureis given by an Adjacency N×N matrix, with a 1 in matrix element i,j ifthere is a connection between nodes i and j. By symmetry, the j,i matrixelement is also 1. Otherwise, for all pairs that are not joined by aline, the matrix element in the Adjacency matrix is 0.

The eigen values of the Adjacency matrix give the energy levels of thequantum network. From this one can compute the “energy jumps” betweenall pairs of energy levels, and from this the distribution of energyjumps, or quanta sizes, in the ER subcritical, critical, orsupracritical=“chaotic” quantum networks

FIG. 3 shows the spectrum of critical, and 2 successively moresupracritical networks, mean ratio lines/nodes=<k>=0.5, 1.0 and 1.5. Allhave giant components which, since they contain most of the nodes,dominate the eigen value spectrum.

These results show that in ER critical and supracritical graphs,position on the x-axis, critical or chaotic, can be attained bymodification of the quantum network structure.

The quantum networks above are structures, realizable, for example, bynetworks of carbon nanotubes capable of quantum behavior. Molecularsystems can also be regarded as quantum networks. Below we discuss twogeneric models of quantum degrees of freedom: quantum rotors and quantumoscillators. It will be clear to those of ordinary skill in the art thatarbitrary graphs can be endowed with quantum oscillators and/or rotorsat, without limitation, some or all nodes, and their quantum andorder-critical-chaos behaviors studied. Without limitation, quantumoscillators can be coupled in arbitrary topologies to one another byinteractions (for example spring-like harmonic interactions). To date,most work has focused, as we will describe, on single “kicked” quantumrotors, or two coupled quantum oscillators coupled by a spring and/orcoupled to a quantum oscillator “heat bath,” as is known in the art.These models are fully extendable to arbitrary networks, as above, asthe quantum system in an arbitrary quantum environment. As discussedbelow, these models, in particular, networks, are suited to modelchemical molecules, will be applied to the evaluation of candidate drugsand the behaviors of nanotube structures.

As noted above, one method of controlling position on the x-axis is tochange the network structure. For example in our application of theseideas to drug design and nano-technology design, a given network canmodel a molecule. By adducting to it another molecule, say by hydrogenbonds or other non-covalent interactions, the graph structure of the newnetwork can be made less than critical, critical, or more supracritical.

We note that networks of more arbitrary structures can be made withcarbon nanotubes or other materials, than can be made with atoms such ascarbon, hydrogen, nitrogen, oxygen, phosphorus, and sulfur, due to thebonding properties of these specific atoms.

Controlling the Topology of the Quantum Networks Via Proximity of theNodes

Consider as a non-limiting example a set of chromophores, parts ofmolecules or independent molecules. Electron exchange is one means oflinking the chromophores, as a non-limiting example.

The details of this interaction depend upon the detailed positions ofthe chromophores. However, in general, if they are sufficiently close,so each chromophore can communicate with many neighbors, many closedquantum loops will exist and the quantum network will be supracritical,hence “chaotic”. If further apart, the quantum network will be lessconnected, and critical or subcritical, moving thereby on the x-axis. Aswe see below, chromophores bound to the membrane of a liposome can bemade more or less chaotic on the x-axis by subjecting the liposome tohypertonic or hypotonic media that shrink or swell the liposome.

As used herein, a generalized “chromophore” refers to any quantumnetwork of interacting elements.

In general, these quantum networks may be on rigid structures such asnanotech devices (e.g, carbon nanotube structures). Or they might beinside or outside or both of a liposome, made as is known in the art, asa bilipid double membrane hollow vesicle, with the chromophores anchoredto the bilipid double membrane via covalent bonding to beta barrelproteins spanning such bilipid layers. The density per liposome ofgeneralized or specific chromophores in the general sense used here canbe tuned through a wide range. As described later in the section onembodied algorithmic or NON-ALGORITHMIC trans-Turing Machinequantum—Poised Realm—classical information processing systems, whichmight be nanostructures or liposomes or other vehicles, liposomes can beconstructed from lipids in water containing the beta barrel proteinswith attached chromophores. One expects a random distribution ofchromophores inside and outside the liposome membrane, allowing such astructure to receive quantum information via the external chromophoresand internal chromophores where light, or other quantum degrees offreedom without limitation, reaches to and across the membrane. The setof all the chromophores form a quantum graph that, together with theliposome and aqueous interior with chosen concentrations of ions andother small and larger molecules, will behave in open quantum, PoisedRealm, and classical ways, as described below, for example withoutlimitation via repeated decoherence and recoherence of quantum degreesof freedom to classicity, which degrees of freedom when classical, orclassical (for all practical purposes, FAPP), will alter both theclassical Hamiltonian of the system, and thereby also alter theHamiltonian of the quantum degrees of freedom. Similarly the recoherenceof a classical degree of freedom, as discussed below, will alter boththe classical and quantum Hamiltonians of the system, hence the totalbehavior of the coupled classical and quantum system over time. Thesefacts are useful in Trans-Turing systems, below.

We also note here that quantum measurement can occur in the PoisedRealm, in the presence of decoherence and recoherence. Measurement maybe achieved, without limitation, by any means. As a central non-limitingexample, the classical degrees of freedom of a system above, as in ourTrans-Turing systems below, themselves constitute part or all of thequantum measuring system which can measure, in some basis, one or moreof the quantum degrees of freedom of the system.

4) Position on the X Axis May be Controlled by Pulsed Stimulation.

A third method to control position on the x-axis (i.e., degree oforder), is by pulsed stimulation. This method may be modeled by a kickedquantum rotor. Basically a quantum rotor is a quantization of aclassical rotor on a frictionless stand that is spinning with somefrequency. If the classical rotor is tapped with “Dirac delta” inputs ofmomentum gently, it remains in the ordered regime, hence left on thex-axis. As it is kicked harder and harder, it moves out on the x-axis,becomes critical, then chaotic. The same holds for quantum rotors as wedescribe below in detail. In the quantum case, the quantum rotor degreeof freedom is kicked with Dirac delta laser light momentum kicks wherethe intensity, “K,” of the kick can be increased, driving the rotor fromorder to chaos. This characteristic is expected to extend to systemshaving arbitrary Hamiltonians. Thus, one embodiment includes modifyingthe state of order or chaos of a system by stimulating the system pulsedlight.

It is expected that quantum rotors or other Hamiltonians kicked toordered, critical or chaotic states will exhibit different quantumenergy level distributions. Thus, measurement of such distributions(e.g., through spectral analysis) demonstrates the degree of order ofsuch a system. Thus we can readily test for position on the x-axis.

For real quantum systems, an issue is at what light frequency to kickthe quantum system. In one embodiment, the center of one or many of theabsorption/emission band(s) of that quantum degree of freedom or a setof quantum degrees of freedom is used for the stimulation.

Degree of Quantum Behavior

For actual physical systems, which can be modeled with quantum networkstructures, the molecular topology of the system can tune thedecoherence rates, and thus movement on the y-axis, in the processesengendered by the system. The electronic energy transfer in chlorophyllis the best example of such a system with both theoretical andexperimental results showing long-lived quantum coherence in anintrinsically noisy cellular environment. Hence the structure ofchlorophyll may play a major role in resistance to decoherence.

Movement from Quantum to Classical Via Decoherence.

Decoherence is a well established phenomenon and the current favoredexplanation of the transition from the quantum to the classical worlds.In quantum mechanics, the signature interference pattern due toconstructive and destructive interference can only occur if all thephase information is present in the quantum system. But in an openquantum system, phase information can be lost from the quantum system tothe environment in an irretrievable way. As this happens, the capacityfor interference patterns in the quantum system decays.

There are at least two ‘as if’ models of decoherence. The bestestablished is the “Lindblad operator”, which allows the off diagonalelements of the density matrix of the system containing the phaseinformation to decay.

A second model of decoherence makes use of a random walk process calledeither a Weiner process, σWdt. In a Weiner random walk process, theWeiner noise term is a random Gaussian variable with mean 0 and avariance, σ. The larger σ is, the larger is the average random phasestep on the orbit in the complex plane of the quantum degree of freedom,such as the quantum rotor.

We have focused in our simulations of the kicked quantum rotor on theWeiner process, but have also used the Lindblad operator. In the Weinerprocess, a variance of 0, σ=0, is “no coherence,” hence quantum on they-axis. As σ increases, the noise increases, and the rate of decoherenceincreases.

In the Quantum Zeno effect, demonstrated experimentally, a quantumdegree of freedom is measured very frequently. Each time it is measured,by von Neumann, it falls to a single amplitude, or eigen state. It thenslowly, quadratically in time, leaves that quantum eigen state and“flowers” to populate nearby and then more distant amplitudes of thatquantum degree of freedom. However, if it is frequently measured, it isalmost certainly “trapped” in its initial quantum eigen state, and thetime evolution of the Schrodinger equation is stopped. As it flowers tonearby amplitudes it becomes a superposition state again, moving up they-axis. So frequent measurements, tunable, can keep a quantum systemnear classical or somewhat quantum because only a small number ofamplitudes have “flowered,” hence control position on the y-axis.

Passing from Classical or Classical FAPP to More Coherent or FullyCoherent, i.e., Down the y Axis.

One embodiment includes driving a system to be more coherent includingdriving a classical system back to quantum. One embodiment includesdriving a classical system into the Poised Realm.

We consider a time independent (autonomous) quantum system described bythe Hamiltonian H under the action of a time dependent externalpotential U(x; t). We can separate the coherent and temporally randomparts U(x; t)=V_(r)(x; t)+V_(c)(x; t). The random part causesdecoherence while the coherent part causes re-coherence in the system.Assuming that the random part is uncorrelated in time and using Ito'srule we can get the time evolution of the averaged density matrix

$\begin{matrix}{{{\partial_{t\; \varsigma}\left( {x,x^{\prime},t} \right)} = {{- {\frac{i}{\eta}\left\lbrack {{\hat{H} + {\hat{V}\; c}},_{\; \varsigma}\left( {x,x^{\prime},t} \right)} \right\rbrack}} - {\frac{1}{\eta^{2}}{\Gamma \left( {x,x^{\prime}} \right)}_{\varsigma}\left( {x,x^{\prime},t} \right)}}},} & (1)\end{matrix}$

where τ(x,x′)=C (x; x)+C(x′, x′)−2C(x, x′) and<V_(r)(x,t)V_(r)(x,t′)>=C(x,x′) δ(t−t′) is the temporal autocorrelationof the random potential at different spatial sites x and x′. In mostrelevant situations a simple discrete Hamiltonian can describe thesystem with matrix elements H_(nm) and the simplest delta correlatednoise can be assumed C_(nm)=Cδ_(nm) and Γ_(nm)=Γ (1−δ_(nm)). Thecoherent external potential, which can come from laser pulses or anyother coherent electromagnetic source, can be reasonably modeled with asequence of sharp kicks {circumflex over (V)}_(c)(x;t)=Σ_(n)V(x)Tδ(t−nT) at times nT.

In absence of the coherent part the evolution of the density matrix isdescribed by

${\partial_{t}\rho_{{n\; m}\;}} = {{{- \frac{i}{h}}{\sum\limits_{k}\left( {{{\hat{H}}_{nk}\rho_{kn}} - {\rho_{nk}H_{k\; m}}} \right)}} - {\frac{\Gamma}{h^{2}}\left( {1 - \delta_{n\; m}} \right){\rho_{n\; m}.}}}$

Decoherence kills quantum superposition states represented by theoff-diagonal elements of the density matrix. The density matrix settlesto the diagonal form ρ_(nm)=δ_(nm)P_(n), where P_(n) is the classicalprobability of finding the system in state n. The characteristic decaytime is h²/Γ˜10−100 femtoseconds. The coherent part is able to re-createsuperposition states. The density matrix before and after the coherentkick is

$\rho_{n\; m}^{+} = {\sum\limits_{n^{\prime}m^{\prime}}^{\;}{U_{{nn}^{\prime}}U_{m^{\prime}m}^{*}\rho_{n^{\prime}m^{\prime}}^{-}}}$

where the unitary matrix U=exp(i{circumflex over (V)}_(c)T/h) describesthe action of the kick on the wave function.

Even if the density matrix is diagonal before the kick Q_(nm)⁻=δ_(nm)P_(n) it becomes non-diagonal after the kick

${\rho_{n\; m}^{+} = {\sum\limits_{k}^{\;}{U_{nk}U_{k\; m}^{*}P_{k}}}},$

indicating the presence of superposition states. Kicking the systemrepeatedly can repair the coherence lost during time evolution and keepthe system levitating at the border of the ‘realms’ of quantum andclassic. The interplay of the coherent kicks and decoherence determinesthe speed of the loss of coherence in the system.

Evidence of that systems can be driven to more quantum behavior includethe following:

1) In the Zeno Effect, the system is trapped in one eigen state, henceclassical during the interval before remeasurement. If not remeasured,the system again flowers multiple quantum amplitudes quadratically intime. One means by which such reemergence of quantum amplitudes happensis in a system which is a quantization of a classical chaotic dynamicalsystem. One of the quantum amplitudes of the localized quantum behaviorsof the quantum system is measured, causing the system to collapse to asingle possibility via the Born Rule and is briefly Quantum Zeno Effect“trapped” in the eigen-state. This amplitude emerges quadratically intime to repopulate other quantum amplitudes with finite moduli.

2) A second means known in the art to regain quantum coherent behaviorconcerns quantum entangled degrees of freedom in a quantum squeezedstate. For specific systems, quantum entanglement can undergo “SuddenDeath”, can undergo No Death, and can undergo Sudden Death and Revival.Such Revival is a revival of coherent entangled quantum behavior fromfar in the classical region (FAPP or entirely classical). We incorporateby reference, “Entanglement dynamics during decoherence”, J. P. Paz, A.J. Roncaglia, Quantum Inf Process (2009) 8 535-548 in it's entirety. Wealso incorporate by reference in their entirety “Entanglement andintra-molecular cooling in biological system?—A quantum thermodynamicperspective.” H. J. Briegel and S. Popescu Phys arXhiv 0806,4552V2[QUANT-PH] 5 Oct. 2009 and “Dynamic entanglement is oscillatingmolecules”, J. Cai, S. Popescu and H. J. Briegel arXhiv:0809.4906v1[quant ph] 29 Sep. 2008. The last two articles computationallydemonstrate and suggest recurrent passage from coherent entanglement toclassical behavior and back. The last paper posits conformationalchanges of a biomolecule induced by interaction of some other chemicalat an allosteric site.

3) A third means known in the art to regain coherence is given by theShor Theorem, which states that in a quantum computer with entangledquantum degrees of freedom, the quantum system can be quantum measuredusing quantum degrees of freedom not part of the qubit calculation.Information can be injected from outside the quantum computer thatrestores quantum coherent behavior to the decohering quantum degrees offreedom, i.e., qubits.

4) A fourth means that induces increased coherence in a quantum orpartially quantum, partially decoherent, and perhaps partially fullydecoherent system almost certainly occurs in chlorophyll wrapped by itsevolved “antenna protein.” At 77 degrees K, the expected time scale fordecoherence is on the order of a femtosecond. The chlorophyll molecule,having been excited by absorption of a photon by an electron, remains inthe quantum coherent (or largely coherent) state for at least 700femtoseconds.

It is believed that this astonishingly long lived coherent state is dueto the antenna protein. This can be experimentally verified by use ofmutant antenna proteins, and this has been done with the antenna proteinand its mutants for a bacterial rhodopsin molecule, where loss ofcoherence occurs with mutant antenna proteins. Long lived quantumcoherence may also be partially due to the quantum graph structure ofchlorophyll.

It may be that the antenna protein entirely blocks any decoherence tothe full environment of the chlorophyll molecule. It is more likely thatthe antenna protein, filled with chromophores, acts on the chlorophyllmolecule by driving it with photons in a physically realized version ofsome type of Shor theorem, to inject information into the chlorophylland sustain or restore coherence to the chlorophyll molecule. Butrestoring coherence means that in physical reality, the antenna proteincan increase coherence in quantum degrees of freedom of the chlorophyllmolecule. The topology of the chlorophyll molecule may play a roleeither in its resistance to decoherence, or ease of recoherence viainput from the antenna protein.

Chlorophyll and its antenna protein is a probable example of a fourthgeneral means to drive a system from classical due to decoherence andphase randomization as above, by kicking the quantum degree of freedomat exactly the natural frequency of any one or a plurality or all of itsquantum amplitudes. Think of a classical rotor whose phase is beingrandomized by modest sized hammer kicks at frequencies that areirrational with respect to its natural frequency. Now hit it with ahammer of tunable size at its natural rotation frequency. You will tendto or will overcome the modest sized hammer irrational “noise” taps andresynchronize the classical rotor. In the same way, consider a quantumdegree of freedom with a sharp band spectrum. Each band is the exactfrequency of light that must hit that quantum degree of freedom withhigh intensity to resynchronize its phase and drive the classical,decoherent degree of freedom down the y-axis through the Poised Realmtoward fully quantum behavior. Almost certainly, the antenna proteinchromophores are doing this, a hypothesis which is testable by mutatingthe chromophores and showing that sustained coherence of chlorophylldecreases then correlating the decreased coherence with a change in theemission spectra of the chromophores on the antenna protein with respectto the absorption/emission spectrum of chlorophyll. This experiment asbeen done with a bacterial rhodopsin and its antenna protein withexactly the above result, although matching to the emission frequenciesof the antenna protein and absorption bands of chlorophyll have not, toour knowledge, been examined.

Additional data has shown that, in a spin bath environment, a quantumsystem can exhibit partial decoherence that levels off with mediumcoherence, in the Poised Realm, where coherent behavior propagating afinite number of coherent amplitudes persists indefinitely. If thesystem is started with less coherence, ie “more classical” in the PoisedRealm, it recoheres to the same intermediate level, propagating a finitenumber of quantum amplitudes coherently. Such stable propagatingamplitudes that persist despite decoherence are useful in quantumcomputation.

As discussed above regarding the degree of order, decoherence can besuppressed and the system kept coherent for an anomalously long time ifit is deliberately kept at the Poised Realm critical transition point.Within the poised realm, ordered and chaotic behavior is associated withrapid exponential decoherence. In sharp contrast, along a critical locusin the poised realm roughly paralleling the y axis and terminating atcriticality on the x axis, poised realm systems decohere much moreslowly, in a power law, not exponential decay of coherence. Thus, withinthe poised realm, criticality preserves coherence better than otherpositions within the poised realm.

Measuring Decoherence and Recoherence Experimentally in Real QuantumSystems.

There is a very convenient measure of decoherence. A dilute gas of asingle atomic species, e.g., hydrogen, has very sharp absorption andemission bands, forming its spectrum. In general, as decoherence setsin, these bands become wider. Thus, the width of a band is a convenientmeasure of the decoherence status of that amplitude of the quantumsystem, which is easy to measure with standard spectrography.

Recoherence can be seen, for example due to driving with light whosewavelength is at the center of a broadened band, by progressivenarrowing of that band. Conversely decoherence and its rate can bemeasured by narrowing and sharpening of the band. And position on they-axis can be measured at any time for any pair of amplitudes whoseenergy gap corresponds to that band, by how narrow or broad it is. Wecan follow position on the y-axis for all pairs of amplitudes of a oneor a system of coupled quantum degrees of freedom on a quantum graph, bythe breadth of such bands. In addition, coherence can be measured usingspin echo experiments.

Our first results modeled decoherence with a Wiener process, σWdt, whosevariance sigma could be altered from 0, hence persistently quantumcoherent in the absence of any decoherence, to infinite, whichrandomizes all phases. Thus, in general, as we move by increasing sigmain the Weiner process, we move from quantum to decoherence to classicalbehavior. For a kicked quantum rotor, position on the x-axis (degree oforder) is determined by the intensity of momentum kicks, of intensity K,to the quantum rotor. These kicks are Dirac delta functions—that is“instantaneous” inputs of momentum energy supplied, without loss ofgenerality, by laser light of any diversity of frequencies, and at anyrate of photon kicks, i.e., intensity K, to the quantum rotor per unittime.

It will be clear to those of ordinary skill in the art, that the photonkicks can be any quantum degree of freedom and delivered with any timeconstant or varying modulated intensity, hence the kicks to each quantumdegree of freedom are a quantum time modulated input signal to thequantum degree of freedom. Therefore, in general, this quantum inputconstitutes quantum information received by the rotor. When wegeneralize to a quantum network with rotors coupled to one another, ormore general systems with quantum and classical degrees of freedom, thiswill become the quantum information via one or a plurality of quantuminputs to a system of quantum and classical degrees of freedom thatresponds to the incoming quantum information, emits quantum informationto its environment, alters its Poised Realm and classical behaviors andalso the quantum and classical Hamiltonians, and constitutes a new classof embodied quantum information processing systems that we callTrans-Turing Systems. Due to the superpositions noted above or purestates and the Born rule, coupled with decoherence to classicality orquantum measurement, the Trans-Turing system is not definite, so notalgorithmic, but due to the classical degrees of freedom and PoisedRealm degrees of freedom, the behavior is also NOT RANDOM IN THESTANDARD SENSE OF QUANTUM RANDOM given by the Schrodinger equation andvon Neumann axiomatization of closed system quantum mechanics. Weemphasize that our Poised Realm systems in general and Trans-Turingsystems are OPEN QUANTUM SYSTEMS, WITH A DISTINCTION BETWEEN THE QUANTUMSYSTEM AND ITS ENVIRONMENT INTO WHICH IT CAN LOSE PHASE INFORMATION.

Decoherence happens in open quantum systems because phase, and alsoamplitude, information is lost from a quantum system, here our singlequantum degree of freedom, to a quantum “environment”. For example aphoton emitted by an excited electron may, on one of its many possiblepaths in Feynman sum over histories formulation of quantum mechanics andquantum electro-dynamics, interact with any quantum degree of freedom inthe environment and thereby induce decoherence.

In our studies of the driven quantum rotor, we model two processes. Wemodel the kicks, K, which hit the rotor once per arbitrary period. Asnoted above, we model the decoherence process as a random walk called aWeiner process, described by σW dt. W is a Gaussian distributed 0 mean,1 variance distribution of “step sizes” which describes the phase changeof the point on the circle in the complex plane at each application ofthe Weiner random walk, during dt. At sigma=0, there is no alteration ofphase, hence no decoherence, and the system is fully quantum. Thus, σWdt=0 is the quantum coherent origin of the y-axis. As σ increases toever larger values, the phase becomes ever “noisier” driven by the whitenoise Weiner process. Thus as sigma increases the rate of decoherenceincreases.

A second way we implement quantum measurement of an amplitude in ouralgorithmic simulations of a Poised Realm system is by taking the squareof its modulus, (i.e., the Born Rule), doing so for all amplitudes ofthe rotor with finite modulus, then choosing one of these amplitudeswith a probability corresponding, via the Born Rule, to its squaredmodulus, and placing the rotor in that single eigen state correspondingto the measured amplitude.

Once the quantum degree of freedom is measured, and in its eigen state,it can leave that eigen state quadratically in time with the “flowering”to finite moduli, of nearby and more distant amplitudes in the absenceof decoherence. In short, at σ=0, no decoherence, full quantum behaviorreemerges with all possible amplitudes for the system. At finite sigma,a finite number of amplitudes with finite moduli will flower as notedbelow.

Quantum Localization of Chaotic Dynamics.

If the classical limit of the quantum system has a Hamiltoniancorresponding a position on the x-axis to the right of the criticalpoint second order phase transition, the classical system exhibitschaos. If decoherence is 0 or low enough, because sigma is low enough,quantum behavior occurs, even in the persistent presence of somedecoherence, but the quantum behavior is localized. In the Poised Realm,only a finite number of amplitudes have finite moduli.

In short, in the Poised Realm FAPP only a finite and tunable number ofamplitudes are present in the quantum behavior of a single quantumkicked rotor degree of freedom, or for any number of independent kickedquantum rotors. The same limited number of amplitudes obtains for kickedquantum oscillators whether single or, if independent, any number.

Energy Scaling of Decoherence.

In our specific, non-limiting example of the use of the Weiner processto model decoherence of any amplitude, we have found that HIGH ENERGYAMPLITUDES ARE ONES MOST LIKELY TO DECOHERE to classical behavior, thatis they become classical degrees of freedom, even for small values ofsigma. By contrast, low energy, small modulus amplitudes do not decohereto classical behavior as readily.

The preferential decoherence of high energy and high amplitude modes isreminiscent of Fermi's Golden Rule for quantum measurement for coherentsystems, where quantum systems tend to take the largest energy drop, egto the ground state, available. But in turn, as exemplified by thefamous photoelectric effect where absorption of a photon, according toEinstein 1905, kicks out an electron from the material, the TRANSFER OFENERGY FROM THE QUANTUM AMPLITUDE TO THE NOW CLASSICAL DEGREE OF FREEDOMWILL BE LARGEST IF HIGH AMPLITUDE HIGH ENERGY AMPLITUDES PREFERENTIALLYDECOHERE TO CLASSICALITY FAPP, OR ARE PREFERENTIALLY MEASURED IN THEPOISED REALM FOLLOWING FERMI'S GOLDEN RULE. This bears on essentialthree topics: i, the efficiency of energy transfer in the Poised Realmand Trans-Turing systems; ii. The use we make below of this preferentialdecoherence of HIGH ENERGY AMPLITUDES to solve the famous FRAME problemin algorithmic computers in our non-algorithmic, non-deterministic, butnon-random Trans-Turing systems—see below. iii. We will use thepreferential decoherence to classicality FAPP or via measurement, belowin Trans-Turing systems such that there is an ongoing decoherence ofhigh amplitude modes to classical behavior, thereby altering theclassical hamiltonian, eg as a non-limiting example by altering thecouplings among classical degrees of freedom. In turn this will alterthe hamiltonian of the quantum degrees of freedom, in turn altering viaconstructive and destructive interference of superpositions, or of purestates, which amplitudes are of high energy and decohere next in time,again altering the classical and quantum hamiltonians of thetrans-turing system. In turn, by recoherence, classical degrees offreedom can recohere, again altering the classical and quantumhamiltonians. This ongoing behavior is the centerpiece of trans-turingnon-determinate, non-algorithmic, yet non-random behavior.

With respect to preferential decoherence of high energy amplitudes, wereason that high energy amplitudes have high angular momentum hence areless affected by random decoherence noise, so we have scaled, as a nonlimiting computational study example, decoherence via the Weiner processto decrease either exponentially or as a power law, with increasingenergy of the amplitude. In particular, we use σ=σ₀ exp (E/Eo) where σ₀is the sigma for a 0 energy amplitude, a constant, E is the energy of anamplitude, and Eo is a scaling factor governing the exponential fall offof Weiner modeled phase decoherence with the energy, E, of an amplitude.

Behavior of a Single Kicked Quantum Rotor in the Poised Realm.

With the above introduction, we find the following: 1) For low enoughsigma and all K, i.e., values of the x-axis, the system is quantum andhas a finite number of modes or amplitudes. 2) As sigma increases, sodecoherence increases and we move up the y-axis in the Poised Realm,there are fewer amplitudes propagating then a transition to classicalbehavior occurs. Thus classical degrees of freedom emerge as decoherenceincreases. 3) The slope of this transition from quantum to classical assigma increases, itself increases as X value, i.e., increasing chaos,increases. That is, more chaotic systems undergo the transition todecoherence more for smaller changes in sigma W than more orderedsystems. 4) There is some indication that the midpoint of the slope ofthis transition to decoherence is “flat” and parallel to the x-axis inthe ordered regime, where decoherence requires similar high sigma W as Xincreases toward criticality, then bends downward in sigma W requiredfor decoherence at criticality, and that decoherence occurs at everlower sigma, i.e., decoherence inducing phase noise, as chaos increaseson the x-axis. This sloping behavior of the midpoint of the transitioncurve means that motion on the x-axis by any means at a constant sigmaW, can move the system from decoherent to more quantum coherentbehavior. For example, decreasing or increasing the intensity of themomentum kicks to the quantum rotor can move that rotor from quantum toclassical behavior and back as the kicks decrease then increase inintensity. Similarly, altering the graph structure corresponding to areal system from critical to supracritical and back on the x-axis canmove the system from coherent to decoherent behavior in the PoisedRealm. We make use of this in the section on drug discovery and actionbelow. This is also true as the Hamiltonian of the system is changed onthe x-axis, which can occur dynamically as a system of coupled quantumand classical degrees of freedom behaves. This constitutes a new way tomove from quantum to classical behavior and back. Thus a single degreeof freedom can be quantum or can be classical, either by tuning theposition on the x-axis by tuning the kick strength K, or by tuningposition on the y-axis by tuning decoherence. So too can a system ofcoupled quantum degrees of freedom, for example in a quantum graph, orquantum and classical degrees of freedom. For example, a criticalchemical quantum network will decohere very slowly, via a power law, notan exponential decay. We have already noted that adducts to a quantumnetwork, or deletions from that network, or alteration in the proximityof generalized chromophores, can alter the effective quantum networktopology on the x-axis moving it to or from the critical locus of powerlaw behavior in the poised realm.

It will also be clear to those of ordinary skill in the art that tuningposition on the x-axis for a single quantum degree of freedom is at ourliberty as it is we who determine kick intensity, K.

Summary of the single kicked quantum rotor in the Poised Realm: 1) onlya finite number of quantum amplitudes grow and have finite moduli. Thenumber of modes decreases as kicking intensity increases. 2) In thechaotic region with high intensity kicking, quantum localization ofchaotic behavior occurs. 3) A transition from quantum to classicalbehavior occurs as sigma W dt is increased, i.e., as decoherence isincreased, but quantum behavior persists for small finite σWdt. 4 Aslope in the transition from quantum to classical behavior along thex-axis is present at some fixed values of σWdt, so any singleindependent kicked quantum rotor can be moved from quantum to classicalby tuning momentum kicking, K, intensity, or decoherence intensity. Or aquantum network can be moved from quantum to more classical behavior bymotion out the x-axis toward chaos, and we believe beyond criticality onthe X axis. Or motion on the x-axis by change of the Hamiltonian of thesystem as quantum degrees of freedom become classical and may, as anon-limiting example, couple in new ways to other current classicaldegrees of freedom, can move the system on the X axis, from more to lessquantum behavior in the Poised Realm. 5) A final feature is thatbehavior in the poised realm is not random, and not Markovian. Thisbehavior partakes of the Anti-Zeno effect, is non-Markovian, hence notfirst order random, as is normal quantum randomness, and is a Floquetprocess. The same conclusions generalize to coupled quantum degrees offreedom or quantum and classical degrees of freedom.

Simulations Using the Lindblad Operator.

As described above, the Lindblad operator is a mean field Markovianmodel of loss of off diagonal terms in the density matrix of a quantumsystem including a single kicked quantum rotor. It is widely accepted asphysically accurate, but is not a detailed “law of decoherence.” Asnoted above, in a Special Relativity setting where the quantum degreesof freedom move with respect to one another there can be no such law.Again, given events A and B, where B is in the future light cone of A,and the past light cone of B includes the past light cone of A, but hasregions space-like separated from A, no observer at A can know whatevents are occurring outside her past light cone. Therefore, there is noway in the Special Relativity setting to write down a law fordecoherence in the space time interval from event A until immediatelybefore event B. In general, there is no “law of detailed decoherence.”

Yet the Lindblad operator, a meanfield approach to the statistics ofthis process, serves well, particularly for tiny relative velocities ofdegrees of freedom.

We have implemented the kicked quantum rotor and increased the frequencyand intensity of kicks, such that they vary from ten times the rotationfrequency of the rotor to its rotational speed, “continuously”. In theordered regime on the x-axis, the finite number of amplitudes is high,and decreases as the critical phase transition is approached. Thus, thebehavior of the system is far from the closed quantum system and unitarypropagation of many amplitudes of the Schrodinger time dependentequation. Only a finite number of amplitudes with finite modulus arepresent.

When the system crosses into the chaotic regime, it becomes fullyclassical. Thus, as in the case of modeling decoherence with a Weinerprocess, sigma W dt, the response of the kicked rotor depends onposition on the x-axis, so the rotor can be moved from quantum toclassical and back by motion on the x-axis.

In this model, the movement on the x-axis is due to the intensity andfrequency of Dirac delta momentum kicks. More generally, the resultssupport the claim that motion on the x-axis back and forth, either bymomentum kicks, quantum network topology alterations by altering networkstructure directly with adducts, deletions, or altering the size, anddensity of generalized chromophores, will alter position in the PoisedRealm.

Evolved organic molecules, like all organic molecules, can exist in thePoised Realm. It will be clear to one of ordinary skill in the art, thatposition in the Poised Realm is likely to affect the behaviors of one ora plurality of molecules, as a non-limiting example, in cells. Thus,position in the poised realm will affect the behavior of drug moleculesas well. It becomes of deep interest if EVOLVED organic molecules occupya specific supspace of the Poised Realm. In particular, we believe thatevolved organic molecules are likely to be at or near the critical locusin the Poised Realm. This critical location allows such evolvedbiomolecules and small organic molecules and drugs to participate in theslow power law decoherence of criticality rather than more rapidexponential decoherence as the system moves further towards order orchaos. Quite interestingly, we will see below that biological smallmolecules appear close to the statistics of the critical giantcomponents in quantum graphs, in our two examples, while cyclichydrocarbons, Buckmeisterfullerenes, graphite and diamond are much morerichly connected and supracritical. This may mean that biologicalmolecules are not purely classical, but may well remain partially poisedin the Poised Realm. The quantum coherent behavior of chlorophyll andbacterial photoreceptor systems is opening the field of quantum biology.Much of cell life may hover in the Poised Realm, with new implicationsfor medicine and drug discovery we return to below.

A means to test whether biological molecules are in the poised realm isafforded by the experiments of Anton Zeilinger, University of Vienna,who has shown that C60 Buckmeisterfullerenes, used as a “beam” in a twoslit experiment, show partial reduction in interference uniformly acrossall interference bands, hence are partially decoherent. This procedureis a new means by which to test the coherence of a particular molecule.In the two slit experiment, molecules will show more or less signaturesof partial decoherence by greater or less reduction of interferencepatterns in the two slit experiment. Thus if there is less than normalinterference, the molecules are in the Poised Realm in a “stable way”.

Drugs in the Poised Realm

It is generally thought that quantum phenomena have no bearing onbiological processes because, at body temperature (about 300K), noquantum phenomena would be present. This view is purely one thatenvisions either a quantum world or a classical world, and the vonNeumann R process of “collapse” of the wave function via the Born ruleto place all the probability on one amplitude with a probability thesquare of the modulus of that amplitude. Quantum chemists have typicallyignored decoherence, treated most of a molecule with classical physicalmodels with a classical Hamiltonian potential, then at most focusedquantum time independent Schrodinger equation analysis of a small“active” part of a molecule, then mathematically “glued” the quantum andclassical aspects of the modeled molecule together.

An interesting failure in this regard, where one of us, Kauffman, hasthe founding patent, is combinatorial chemistry (See Kauffman Ballivetpatents 1986 France to 1992 US). The US pharmaceutical companies havespent billions making libraries of more or less random organic moleculesthen screened these for ligand binding to shape complements of desireddrugs. For example, a random organic molecule binding to the estrogenreceptor, like a random key fitting the receptor thought of as aclassical physics “lock”, is a candidate to shape mimic estrogen itselfand hence be a drug candidate. This entire approach, which Kauffman andBallivet invented, treats ligand binding pairs as fully classicalphysical entities, locks and keys, the then prevailing theory. Theapproach has failed. The drug companies in the US are said to havenearly empty drug pipelines. By contrast, the Japanese pharmaceuticalcompanies continued over the past decades, we are told, to rely ontraditional medicinal chemistry and they have many drugs in theirdevelopmental pipelines. This sharp contrast suggests that the medicinalchemists were unwittingly probing the Poised Realm behavior of drugcandidates and combinatorial chemistry with its screening orcomputational designs based largely on classical physics models of allor most of the candidate molecule's structure and dynamics, missed anyPoised Realm behaviors relevant to drug action. This bears on our use ofthe Poised Realm for drug discovery, as well as for understanding basiccell biology.

In the standard view, the world is either fully quantum or fullyclassical. There is no notion of a Poised Realm between quantum andclassical. As described above, data demonstrates that there is in fact aPoised Realm between fully quantum and fully classical. As an example,the long term quantum coherence of chlorophyll is galvanizing quantumphysicists and a new field of quantum biology. The antenna protein andits chromophores almost certainly cannot block decoherence fromchlorophyll. There is further evidence in the prior art that moleculartopology within chlorophyll can serve to slow down the rate ofdecoherence either by making chlorophyll more readily subject torecoherence via the antenna protein or chlorophyll itself, or in itself.It seems probable that both the structure of chlorophyll makes it moreeasily subject to recoherence and the antenna protein mediates this“recoherence,” perhaps by photons absorbed in the center ofchlorophyll's absorption band(s).

Beyond chlorophyll, quantum events in biology are evidenced by quantumcoherent electron transfer demonstrated in quantum chemistrycalculations, and it appears to play a role in cells in that, as thedistance between two proteins increases, electrical conductivity fallsoff, but shows a plateau in electrical conductivity at a distance ofabout 12 angstroms to 15 angstroms. Conductivity falls off as distanceincreases. 12-15 angstroms is just the distance that allows a watermolecule to hydrogen bond between two proteins and afford two pathwaysof electron transfer, hence in analogy with the two slit experiment,allows quantum interference patterns. The work on electron transfer byD. Salahub and colleagues at the University of Calgary, has shown such abound water molecule and coherent electron transfer between twoproteins. The cell is a densely crowded matrix of proteins at about the10-15 angstrom distance, with an abundance of coordinated water betweenthem. This invites the hypothesis that percolating connected pathways ofelectron transfer within and between the proteins in the cellcytoplasmic matrix occurs. This may allow extensive quantum coherentbehavior in cells. Similar evidence in bird navigation by quantumbehavior in molecules of their eyes picking up earth's magnetic field.More generally quantum biology is exploding, BUT IT REMAINS FOCUSED ONQUANTUM COHERENT BEHAVIORS. We believe quantum coherent behaviors arethe literal tip of the iceberg in quantum biology, with many or mostquantum effects in the Poised Realm of open quantum systems in anenvironment to which they can lose phase information, where quantumcoherence is a limiting boundary of the Poised Realm. This bears on drugdiscovery and action, and molecular behaviors in cells and tissues andorgans and the whole organism.

The electrons in such electron transfer within and between proteinswith, or without such a percolating web, exchange electrons all thetime. This implies that such electrons may induce recoherence, theQuantum Zeno Effect, and Quantum anti-Zeno effect on otherwisedecohering quantum degrees of freedom in cells. Thus, cells may, to asubstantial extent, live in the Poised Realm. In addition, drugs near orat the critical locus in the Poised Realm will participate in the slow,power law decoherence at criticality, rather than the ever fasterexponential decoherence further from criticality toward order or chaos.All this concerning position on the X axis at least, will affect drugbehavior in general and in vivo in particular. We believe this is ofextraordinary importance.

But criticality in the poised realm has universal behavior associatedwith power law decoherence, not exponential decoherence. If slowdecoherence is useful biologically, then critical location in the poisedrealm is useful. As noted above, a comparison of random organicmolecules and evolved organic molecules tests whether evolved organicmolecules are in a special, perhaps critical, location in the PoisedRealm. Whatever the answer may be, it is a huge clue to effective drugdesign and action.

Molecules can behave in various reactions differently depending on wherethey are on the chaos-order (x) and quantum-classical (y) axes. Theirposition is an important characteristic which can be used in chemicaland drug design. The position of a molecule on the x axis can bedetermined from the energy level spacing distribution as it wasdescribed for general systems before. Experimentally, the levels can bereconstructed from the excitation spectrum as it is known to the art,their mean level spacing Δ(E) as a function of energy can be fitted andthen the distribution of spacings s_(n)=(E_(n+1)−E_(n))/Δ(E_(n)) can beanalyzed.

$x = \frac{A - A_{p}}{A_{w} - A_{p}}$

can serve as the x-coordinate where the quantity A is calculated fromthe actual level spacing of the system

A = ∫₂^(∞)p(s).

The position on the y axis can be calculated from the Hamiltonianoperator of the molecular system and its interaction matrix elementswith the environment as we described earlier. In reality, from the pointof view of molecular design the most important property is not the ycoordinate position directly, but the distance of the molecular systemfrom the critical poised realm state. This distance can be determinedfrom the results of the decoherence measurements, e.g. form the outputof the relevant echo type measurement. In molecular systems this isusually photon echo or neutron spin echo measurement. The result of theecho measurement is a signal S(T_(E)) where T_(E) is the echo time (timebetween the first and the second pulse as known to the art). Fornon-critical systems the long time behavior of the signal is exponentialS(T_(E))˜exp(−T_(E)/T_(D)) where T_(D) is the dephasing time, whichserves as our coherence time FAPP. For critical PR molecular systems thedecay of the signal is a power law S(T_(E))˜T_(E) ^(−α) with someexponent α, which can be determined from fitting the experimental curve.Systems in general are usually not exactly in their critical state,therefore the ultimate decay of the signal is exponential. However,depending on their closeness to the critical state a transitional formS(T_(E))˜exp(−T_(E)/T_(D))/T_(E) ^(α); can be fitted to the curve andthe parameters T_(D) and α can be determined. In case of changing theparameters of the molecular system via changing the macroscopicparameters, applying external forces (for example laser light)transition towards the critical poised realm state can happen. Changetowards the critical state is reached in a diminishing of the dephasingtime T_(D)→0 determined via fitting the transitional form to theexperimental echo signal. The value of α can change during the parameterchange but it remains finite during the process. The measured value ofT_(D) is a good measure of the distance from the critical state. Thesmaller the T_(D) the closer the system to criticality is.

Beyond simple parameter change the position of the molecular system canbe changed by making changes is its configuration. Adding or removingsome parts of a macromolecule or changing its structure by anymanipulation can change its position within the poised realm.

As discussed above, degree of order (i.e., position on the x-axis of thepoised realm model) can affect the decoherence rate of a quantum degreeof freedom. For example, at the critical transition point of the degreeof order (discussed above), the decoherence rate is suppressed. Whilenot being bound by any particular theory, it is proposed that biologicalsystems, and hence biological activity, operate optimally at particularrates of decoherence. In some embodiments, certain biological systemsoperate optimally where the decoherence rate is slow. In otherembodiments, certain biological systems operate optimally at fasterdecoherence rates. Accordingly, for a particular biological system(e.g., a particular enzyme or receptor), the best drug molecules will bethose having a particular degree of order (i.e., position on thex-axis).

Some embodiments provide a method of drug discovery that seeks toidentify drug molecules that particular targets based on the molecules'position on the axis. One such embodiment is described with reference tothe flowchart of FIG. 4. This method seeks to identify the mostpromising drug leads for a particular target from a library ofcompounds. Identification of drug leads from libraries of compounds is acommon approach to drug discovery; however, such approaches rely oneither molecular modeling methods (e.g., ligand docking) or in vitroassays. Most compounds identified as promising by such methods oftenprove to be ineffective and/or toxic and are ultimately never developedinto a drug. The present method provides an alternative approach.

Libraries of compounds to be used with the present method may beobtained using known means, for example, generated using combinatorialchemistry approaches or commercially available. At block 500 of FIG. 4,a particular biological target (e.g., an enzyme or receptor) isselected. At block 510, a molecule from the library is tested forbinding to the target. Traditional methods of binding detection may beused, including in vitro binding assays and in silico modeling methods.If the test molecule binds to the target, it proceeds to the next step.If not, a new molecule from the library is selected at block 520 and istested for binding.

At block 530, the energy level spacing distribution of a quantum degreeof freedom in the molecule is determined. This distribution may bedetermined using known methods including experimentally (e.g., usingspectroscopic techniques) or theoretically using known modelingalgorithms. In some embodiments, the determination of energy levelspacing is determined as it would be in the biological environment(e.g., while the molecule is bound to the target). Once the energy levelspacing distribution is known, it may be compared to reference functionsat block 540 to determine the degree of order (i.e., position on thex-axis) of the molecule. For example, as described above, in a pureordered regime, the energy level spacing distribution has the form:

p(s)=exp(−s)

where s is the energy level spacing and p(s) is the energy level spacingdistribution. In a purely chaotic system, the distribution has the form:

${p(s)} = {\frac{\pi \; s}{2}{\exp \left( {{- \pi}\; s^{2}\text{/}4} \right)}}$

The actual distribution of the test molecule may be compared with thesefunctions to determine its position on the x-axis, for example, using

${x = {{\frac{A - A_{p}}{A_{w} - A_{p}}\mspace{14mu} {where}\mspace{14mu} A_{p}} = {\int\limits_{2}^{\infty}{p_{p}(s)}}}},{A_{w} = {\int\limits_{2}^{\infty}{p_{w}(s)}}},{and}$${{A = {\int\limits_{2}^{\infty}{p(s)}}},{{{where}\mspace{14mu} {p_{p}(s)}} = {{\exp \left( {- s} \right)}\mspace{14mu} {and}}}}\mspace{14mu}$${p_{w}(s)} = {\frac{\pi \; s}{2}{{\exp \left( {{- \pi}\; s^{2}\text{/}4} \right)}.}}$

p(s) is the actual distribution for the test molecule.

At block 550, it is determined if the energy level spacing distributionof the test molecule has the desired relationship to the referencefunction. This relationship may be a pre-determined value for x found tocorrelate with high activity or in some embodiments, is the relationshipthat indicates that the molecule exists at the critical transition pointalong the x-axis. As discussed above, this critical point may bedetermined by the energy level spacing distribution having the form:

p(s)=4sexp(−2s).

Thus, in some embodiments, molecules are selected at block 550 that areclose the critical transition point as determined based on their energylevel spacing distribution.

If a candidate molecule has the desired relationship as determined atblock 550, it is selected as a drug candidate at block 560. If it doesnot, the procedure returns to block 520 for the selection of a newcandidate from the library. Drug candidates selected at 560 maythemselves be suitable for drug development or, alternatively, may serveas lead compounds for further optimization using known quantitativestructure active relationship (QSAR) medicinal chemistry. In someembodiments, new candidates based on the selected lead compound are alsoscreened following the method in FIG. 4 to determine if they have thedesired degree of order and are thus suitable drug candidates.

A variation of this method is described in the flow chart of FIG. 5.Again, a library of compounds is provided and biological target isselected at block 600. The candidate molecules are checked for bindingto the target at block 610. If binding is not observed or predicted, anew candidate is selected at block 620. If binding is observed orpredicted, the energy level spacing distribution is determined at block630. Next, an in vitro and in vivo biological assay is performed todetermine the activity level of the compound at block 640. Thisprocedure may be repeated for a number of molecules in the library suchthat a correlation may be made at block 650 between the energy levelspacing distribution and biological activity for the particularbiological target. The correlation may be between a determination of aparticular degree of order (e.g., position on the x-axis) or may be aparticular energy level distribution obtained, for example, by averagingthe distributions of the most active compounds.

Once a suitable correlation is constructed, a new candidate molecule maybe tested without having to perform an experimental assay for biologicalactivity. In this case, the energy level spacing distribution of the newcandidate may be determined at block 660 using known methods. Thisdistribution is compared at block 670 to the correlation determined atblock 650. The comparison may include directly fitting the distributionto average distribution for previously determined active compounds ormay include determining the degree of order (e.g., position on thex-axis) as described above and comparing that determination to the knownactive compounds. If a close match is made, that molecule may beadvanced as a drug candidate at block 680. If not, a new candidatemolecule may be selected at block 690 and evaluated in a similarfashion.

In some embodiments, the rate of decoherence of candidate molecules maybe directly measured using known methods including spin echo techniquessuch as nuclear magnetic resonance spin echo, neutron spin echo, orphoton echo. These techniques can be particularly useful to evaluatemolecules within a biological environment (e.g., bound to a target inpart a biological mixture, for example, a cellular extract mixture). Inthese embodiments, the above methods may be modified such that ratherthan determining and comparing energy level spacing distributions,candidate molecules may be tested for a desired rate of decoherencerate. For example, in one embodiment, candidate molecules that bind tospecified target may be evaluated to identify the molecule having theslowest rate of decoherence. In one embodiment, the experimentallymeasured decoherence rate is fitted to the functional formS(T_(H))˜exp(−T_(H)/T_(D))/T_(H) ^(α) and the value of T_(D) determined.In one embodiment, selection of a drug candidate includes selectingmolecules having low T_(D) values.

Another embodiment considers the modeling of molecules using quantumnetworks. We use as a NON LIMITING example of quantum networks, taken asmodels representing real organic molecules, and as crude examples, theErdos Renyi random graphs described above. FIG. 6 depicts an example ofa 100 node exactly critical Erdos-Renyi graph, and typical GiantComponent containing 83 of the 100 nodes. A critical ER Giant Componentof 47 of 50 total nodes is shown in FIG. 7. The 83 node Giant componenthas 28 nodes with <k>=1 connections, 11 nodes with <k>=2 connections totheir two neighbors, 14 nodes with <k>=3 connections to threeneighboring nodes and five <k>=4 nodes connected to four neighbors. Theratio of bonds, or lines to nodes, i.e., bonds/nodes=1.349. The 50 nodeER graph with a critical 47 node Giant Component has eleven <k>=1 nodes,eleven <k>=2 nodes, six <k>=3 nodes, six 6<k>=4 nodes, and seven <k>=5nodes. Its mean <k> is 2.34. The mean of these two is <k>=1.8445. We donot know the mean and variance of connectivities for critical GiantComponents of Erdos-Renyi graphs, but presume that these two are roughlytypical, probably on the low and high side of the mean <k> for suchcritical Giant Components.

Preliminary analysis suggests that biological small molecules, andperhaps proteins and nucleic acids and lipids, are very similar in theirmean <k> values to the Giant Component of critical Erdos Renyi graphs.In contrast, many organic molecules not found in life seem to have ahigher <k>, characteristic of the supracritical, or chaotic quantumgraph regime. This analysis treats single, double and triple covalentbonds the same and counts only connections among pairs of atoms.

A small sample of non-biological organic molecules include thefollowing: Napthalene <k>=2.2; Anthracene <k>=2.214; Methylpropane<k>=4.0; DiMethylpropane <k>=4.0; Cyclohexane <k>=4.0; Annulene <k>=2.0;Buckminsterfullerene <k>=3.0; and Diamond, <k>=4.0.

Over a random sample of 20 biological small to medium sized organicmolecules, the mean value of <k>=1.928. While the sample of ER giantcomponents is only two and we do not know the true mean of all possibleER giant components, their average, 1.8445, is close to that for thebiological organic molecule sample (<k>=1.928). The spread in <k> valuesamong the 20 biological organic molecules is very narrow. The 20molecules and their <k> values are: acetate 1.66, caffeine 1.96,abscisic acid 1.88, acetic acid 2.0, acetylcholine 1.555, adrenaline2.0, alanine 1.875, arginine 1.925, asparagine 1.72, bacteriopheophytinA 1.983, B carotine 1.987, catechol 2.0, estrone 2.09,fructose-6-phosphate 2.0, glucose 1.965, histadine 2.04, isoleucine1.92, lactose 2.0, phenylalanine 2.0, retinoid acid 2.0.

As noted, we do not yet know the mean and variance for the connectivityof the giant component among all critical Erdos-Renyi graphs. Presumablythe true mean is near the mean of our two critical Erdos Renyi Giantcomponents, <k>=1.8445. The narrow spread of biological organicmolecules is striking, as is the close agreement between the two means,Erdos Renyi critical Giant components, and these biological smallmolecules.

Proteins and nucleic acids and lipids and polysaccarides seem likely tobe close to critical in their covalent bond structure, again ignoringthe distinction between single, double and triple bonds in favor of“connections between atoms.” They are comprised of smaller componentsthat are near critical.

These observations suggest that natural selection has tuned the positionof biological molecules on the x-axis to be very close to criticality,with a very narrow range of <k> values, and we suggest below why thismay be deeply useful in drug design and discovery. In turn, theseobservations suggest that cells live, due to natural selection,partially poised in the Poised Realm between fully quantum and fullyclassical and, like chlorophyll, natural selection has made good use ofthe Poised Realm.

We note that in a preferred embodiment of this invention, we canexperimentally test whether random and evolved organic molecules arelocated, respectively through larger regions of the Poised Realm forrandom organic molecules, and whether evolved organic molecules areCRITICAL IN THE POISED REALM, by their rates of decoherence. Criticalmolecules will decohere in a power law distribution, as described above.Thus, using line band broadening as a measure of decoherence,spetroscopic means known in the art, or any other means now or in thefuture known to measure decoherence, we can measure an organic moleculeto look for power law decoherence as a signature of the criticallocation and behavior of said organic molecule. Thus we can test,without limitation, any organic molecule for exponential decoherence ifordered or chaotic in the Poised Realm, or power law decoherence ifcritical in the Poised Realm. Without limitation, we can test ifchlorophyll and its antenna protein are critical in the Poised Realm bytesting for power law decoherence. Thus, in general, we can test whetherevolved biological molecules are critical or near critical, while randomorganic molecules or other molecules are not critical in the PoisedRealm. This is of general relevance to drug action and thus to drugdesign. Testing for power law decoherence or exponential decoherencemay, without limitation, be made in vivo or in vitro.

A striking feature of our studies of the kicked quantum rotor using theLindBlad operator is that as kicking intensity and frequency increase,the rotor passes from the ordered regime with a large but finite numberof quantum amplitudes with finite moduli, to fewer amplitudes withfinite moduli as criticality is approached, to a sudden jump toclassical behavior when the critical line in the Poised Realm is passedand chaos is entered on the x-axis. But when the system passes fromquantum to classical behavior: i. energy is transferred from the quantumto the classical world. ii. The now classical degree of freedom can haveCLASSICAL PHYSICS effects on the classical world! The poised realmsystem can then ACT on the classical world. iii. Position near thecritical line maximizes passage back and forth from quantum toclassical, thus the diversity of classical actions the system can take,based on Poised Realm “calculations” in the quantum aspect of the poisedrealm, which is non-determinate, non-algorithmic and not random! We usethis in Trans-Turing systems below as well.

The quantum network models discussed above are not yet endowed withquantum degrees of freedom such as quantum rotors or oscillators attheir nodes, with coupling between, e.g., quantum oscillators viasprings along the arcs of the network. Ease of decoherence for quantumsystems described by classical Hamiltonians, depends upon the averageLyapunov exponent, which is 0 in the ordered regime and bifurcates atcriticality to a positive value, where decoherence occurs more readily.This invites the hypothesis, supported by our theorems above about powerlaw decoherence for critical quantum systems, which we can testcomputationally, that critical quantum networks with, for examplequantum oscillators at the nodes and coupled by springs, decohere lesseasily than do supracritical or ordered quantum networks with suchcoupled quantum oscillators. If the hypothesis is proved, we suspectthat small evolved biological molecules, and hence also bioactive drugs,may live poised partially in the Poised Realm and be able to behaveclassically by increasing <k> via, e.g., hydrogen bonds where theybecome both subject to rapid decoherence, and behave classically bycrossing the critical line on the X axis into chaos and decohererapidly. We recall the evidence that decoherence can alter the rate of achemical reaction.

Based on the foregoing, there are two implications for drug discoveryand drug action:

1) A drug, when quantum coherent cannot ACT calssical. Thus, we can“turn off” a drug by inducing quantum behavior either by recoherence onthe y-axis of the Poised Realm, or lowering <k> values than about 1.8445(i.e., moving on the x-axis of the Poised Realm toward criticality andpower law slow decoherence rather than rapid exponential deochrence).And conversely, we can turn the drug “on” again by inducing decoherenceas in the Quantum Anti-Zeno effect, or transition to chaos andclassicity by increasing <k> and moving <k> to be greater than 1.8445,to supracritical quantum network molecular structures and dynamics inthe chaotic regime on the x-axis of the Poised Realm. Here the moleculeremains connected, ie<k> equal or greater than 1.0, and at a positionfurther out the X axis than criticality, decoheres exponentially rapidlyto classicality FAPP or by measurement, hence becomes classical and canhave classical effects on the classical world of the cell or organ.

2) We can design drugs which are critical on the x-axis. Indeed, drugmolecules are open to a statistical study to see the mean and varianceof their <k> values. Improved drugs may be obtained by tuning <k> tocriticality for at least two reasons. First, if small molecules in cellsare near the quantum classical boundary, due to natural selection, it isbecause their classical physics action requires crossing that boundaryback and forth. Then drugs would seem likely to act more efficiently ifthey could participate in such action. Note that this is in strongcontrast to designing drugs using classical molecular dynamic models ofmolecules with classical potential functions then docking the classicalmodel molecules with classical ligands. This may be a roughapproximation to a dance of quantum-classical transitions in the PoisedRealm by small molecule effectors, natural or drugs, acting on larger,supracritical, more classical target ligands. In short, small moleculesand drugs may perform best if poised in the Poised Realm between quantumand classical behavior, able to become classical by hydrogen or van derWaals forces to ligands, altering <k> into the supracritical, chaotic,classical behavior regime. It follows that drugs can act by having <k>values that are lower than critical ER giant component graphs, or moreaccurate than ER, chemical network structures we can use for drugdesign, and by ligation to a target, lower the total <k> value movingtarget+adduct to lower X values, hence more quantum behaviors toinactivate the target+adduct molecule by altering from classical toquantum behaviors. This is in stark contrast to the standard view of adrug as a classical object binding to and blocking binding of a smallmolecule to a target molecule, e.g., blocking estrogen from binding tothe estrogen receptor. Here, instead, estrogen may be made more“quantum” by binding a drug to estrogen itself, lowering its <k> value,so it less readily becomes classical on binding the estrogen receptor,and hence is unable to act. Conversely, to increase the activity ofestrogen, we might seek to increase its <k> value by an adduct thatincreases estrogen+adduct mean <k>, so the total system becomesclassical more readily by motion outward on the x-axis.

Thus, the Poised Realm affords a truly new way to think about blockingor activating biological drug target molecules, quite independently, ortogether with, binding to the “binding site” of the target considered asa classical molecule. Importantly, moving the target+adduct to a lowermean <k> than critical, hence more rapid deochrence may be feasible byadducts that bind at MANY sites on the target, e.g., without loss ofgenerality, estrogen molecule, IN ADDITION to also binding in thebinding site of estrogen. Then the number of ways to “block” the actionof estrogen, or by making estrogen+adduct more classical hence enhanceestrogen's activity, are likely to be increased compared to classicalconsiderations of blocking only the binding site of estrogen. Thus manymore candidate drugs per target become possible.

In further consideration of the above, an adduct binding not necessarilyat, but also near the binding site of a larger molecule, such as theestrogen receptor as a nonlimiting example, may alter the local quantumPoised Realm behavior of that part of the receptor, rendering it morequantum, hence blocking the receptor from binding, or becoming moreclassical hence rendering it more able to bind. Again the number ofdrugs that may bind near the binding site and accomplish this adds tothose that classically bind the binding site, and so increase the numberof potential drugs affecting estrogen-estrogen receptor interactions.

With respect to turning a drug on or off, some embodiments includestopping and starting the activities of roughly critical small moleculesin the cell by inducing recoherence via, without limitation, laser lightin their absorption bands. Organic biological molecules often absorb inthe infrared and very far infrared. Infrared radiation, about 1000-3000nanometers, can penetrate substantially into the human body. Thus we caninduce recoherence of small molecules in the body, using the informationobtained from the specific absorption and emission spectrum of eachsmall organic molecule, and hence directly “address” specific moleculesin the body to affect the quantum or classical or Poised Realm behaviorof that specific molecule in the body. Some embodiments use energyranges that reach only the skin or a bit under it (e.g, using visible,infrared, or far infrared light). Other embodiments use light thatpenetrates more deeply (e.g., using longer wavelengths, with the obviousproviso that damage to tissues must not be done). Avoiding damage may beobtainable in general by modulating the timing and spectral distributionfrequencies of the incident photons.

Similarly, given a drug that is, roughly, critical, some embodimentsincrease its “classical” action by inducing decoherence via theAnti-Zeno effect or generalizations, or decrease its effect by inducingrecoherence by driving its quantum degrees of freedom with, withoutlimitation, laser light in the infrared or longer wavelengths, where thedrug has absorption bands, or for topical skin treatment or othertopical treatments, with light in the visible.

The above use of recoherence and decoherence to tune a drug's positionin the Poised Realm can be used to obtain optimal drug action bycontrolling behavior in the Poised Realm.

Thus, small molecules and drugs may act best, not classically, but bybeing poised in the Poised Realm where a smooth transition to classicityis achieved upon binding adducts to move the drug further toward orderand quantum Poised Realm behavior. This may allow the drug to graduallyanneal to a classical or near classical Poised Realm state in binding tothe larger protein or other drug target. We can tune this annealing bytuning where the drug is on the x-axis and by infrared radiation to tunedecoherence and recoherence.

Furthermore, like real annealing where a metal is heated, hammered, thenquenched repeatedly so that it finds micro-crystal rearrangements toever deeper potential wells and becomes and ever harder metal, and inanalogy to simulated annealing in a finite time using both “cooling” and“heating” to tune the free energy surface to avoid poor local minima ona classical potential, we can “anneal” repeatedly our drug to its small,perhaps critical, or larger more supracritical target. In particular,upon binding to a supracritical target ligand, a small critical drug,will, through hydrogen bonds, become on average more supracritical,hence classical, and “freeze” into a more rigid behavior, but indecohering make use of the Poised Realm quantum behaviors which canexplore quantum possibilities and find good potential wells. Byrepeatedly inducing coherence with infrared radiation, then allowingdecoherence multiple times, a better ultimate binding of drug to targetmay be obtainable.

Finally, if drug and target are both roughly critical where decoherenceis power law slow and not exponential fast in the ordered and chaoticregimes, and partially in the Poised Realm, we can use infrared tolonger wavelengths radiation, as noted above, to help preventdecoherence and sustain the Poised Realm behavior not sustainable byphoton showers from within the cell.

Determining Coherence and Order of Candidate Drug Molecules.

As discussed above, degree of order can be determined by theabsorption/emission spectrum of a drug or organic molecule via the levelspacing distribution. The degree of coherence can also be determined byabsorption band widening due to decoherence. If critical quantummolecules decohere less easily than supracritical ones like polycyclichydrocarbons, the critical molecules and presumably small biologicallyactive organic molecules with <k> near 1.8445, or more realisticchemical structures, should show less band broadening than polycyclichydrocarbons or Buckmeisterfulerenes with <k>=3. More,Buckminsterfullerene or other X axis chaotic molecules may decohereexonentially and more rapidly exponentially as they are more chaotic, soexhibit a Quantum Anti-Zeno effect more readily than critical organicmolecules. So too may polycyclic hydrocarbons compared to more criticalorganic molecules subjected to natural selection.

Finally, we can assess criticality, subcriticality or supracriticalityon the x-axis for the molecular structure of a drug, adduct, target, anddrug+target or drug+adduct+target, via the eigen value spectrum of itsadjacency matrix for its energy levels, from which one can deduce theabsorption and emission spectrum of the above drug, drug+target, ordrug+target+adduct. These predictions can then be tested experimentallyby measuring absorption bands by any means known in the art.

It will be clear to those of ordinary skill in the art that it ispossible to test any molecule, or set of molecules in an assemblage fortheir position both on the X axis alone and in the poised realmgenerally. Here we use three independent approaches, alone or together.First, we use a quantum network model to determine position of anymolecule on the X axis, hence also any set of independent molecules.Second, we measure the absorption and or emission spectrum distributionto establish, as noted elsewhere in this patent application, theposition of the molecule or molecules, on the X axis. Third, we measurethe decoherence rate, ranging from a power law for a critical positionon the X axis to an exponential whose rate can vary on the X axis, andto intermediate decay forms that are mixtures of power law andexponential behaviors as described in this patent application.

It will be clear to those of ordinary skill in the art, that if themolecule being studied or set of molecules being studied are behaving ina classical fashion, they can be stimulated by any means known in theart, including appropriately tuned laser wavelengths, as described inthis patent application, to behave in the Poised Realm, or quantumcoherent behavior may be obtained in the limit of total recoherence orreflowering of quantum amplitudes. It may often be necessary tostimulate such Poised Realm behavior to assess experimentally byabsorption/emission spectral distributions and decoherence rates, theposition of the molecule or a set of molecules on the X axis.

However, in general, organic molecules are quantum in their behavior asis well known in the art to spectroscopists, hence no stimulation as inthe above paragraph will typically be needed.

In general, if the absorption/emission spectra of the differentmolecules are all uniquely different the set of molecules can bemeasured for their position on the X axis simultaneously by measuringthe spectra of each molecule and the total set of molecules.

More generally, for assemblies of molecules, the absorption/emissionspectra may reflect inter-atomic or inter-molecular interactions, butboth the absorption/emission spectrum of the assembly, and itsdecoherence rate can still be measured to asses the position of theassembly as a whole on the X axis. Here if there is a distribution ofpositions on the X axis by different parts of the assemblage, this willshow up as different absorption/emission spectral distributions by thedifferent components of the assembly. These can be deconvoluted,trivially if the spectral lines for each molecule are unique, and thosedue to inter-atomic and inter-molecular interactions are unique for anypairs of molecules or small interacting subsets of molecules in theassembly. More complex spectral distributions can also be deconvolvedbecause we know the ratios of the different molecules and their bindingpartners in the assembly, without limitation, a macromolecular assemblysuch as a neurotransmitter receptor and its complex of molecules in asynapse.

With the above, we can study drugs that are known to be effective,and/or evolved biomolecules, compared to random and in particularunevolved organic molecules to test the locations of in vitro or in vivodrugs or evolved organic molecules on the X axis and in the PoisedRealm, compared to “random” organic molecules. In one non-limitingexperiment, unevolved organic molecules from chrodronaceous meteorities,such as the famous Murchison meteorite, which has been shown to have atleast 14,000 distinct organic molecules, are used to test differences inthe poised realm between evolved and unevolved molecules. Since themeteorite dates from about the origin of the planet earth, thesemolecules are clearly abiotic. In addition, collections of known naturalabiotic and synthesized organic molecules are widespread, including inBeilstein, and in the libraries of pharmaceutical companies, including,without limitation, combinatorial chemistry libraries. In addition, weincorporate by reference Origins of Order by Stuart Kauffman, OxfordUniversity Press, which describes a means to generate large libraries oforganic molecules titled “random chemistry” which can be used to obtainunevolved organic molecules.

In one experiment, approximately 1500 FDA approved drugs available fromthe Johns Hopkins Chemical Compound library is used to determine howthey cluster in the poised realm. Specifically, the position on thex-axis of the poised realm is determine using methods described hereinfor each of the 1500 approved drugs. These are in turn compared to arandom library of compounds, such as those available from compounddatabases (e.g., Beilstein) or from the Murchison meteorite. Theexperiment can demonstrate whether molecules having drug action clusteraround a specific value on the x-axis. For example, they may clusteraround the critical point discussed above.

Quantum Reservoir Computer

One embodiment utilizing a system operating in the poised realm isquantum reservoir computer, which is an embodied quantum variation of aclassical reservoir computer known in the art. In this embodiment, thenodes within the reservoir are physical entities having at least onequantum degree of freedom that is capable of coupling (e.g., viasuperposition of states) to quantum degrees of freedom in other nodes inthe reservoir. Unlike current quantum computers that utilize qubits, aquantum reservoir computer does not require that all elements (i.e.,nodes) in the reservoir be fully quantum coherent. Rather, the quantumparallelism in the system is exploited in a self-organizing manner.Thus, the system can, in some embodiments, operate at room temperature.

The reservoir of the quantum reservoir computer can be viewed as acollection of weakly interacting discrete quantum degrees of freedom.The reservoir may comprise any fixed number of physical entities(referred to herein as “nodes”) having at least one quantum degree offreedom. In one embodiment, the nodes are chromophores, which mayincluding a biological chromophore such as a photosynthetic unit (e.g.,chlorophyll, with or without it's accompanying antenna proteins), anon-biological organic chromophore (e.g., highly conjugated organiccompounds), or an inorganic chromophore such as an inorganic metalcomplex. In one embodiment, chromophores are selected having arelatively long, but finite, coherence lifetime (e.g., as is found inchlorophyll).

In another embodiment, the nodes in the reservoir are spins or magneticmoments. Any known spin or magnetic systems may be used, including forexample paramagnetic or ferromagnetic compounds or nanostructures. Inone embodiment, an artificial spin system such as is the commerciallyavailable in the D-WAVE system may be used, which utilizessuperconducting current to simulate spins.

In some embodiments, the quantum reservoir can be tuned to achieve adesired coherence time. For example, decoherence may be added byapplying a random noise potential. The system may be tuned into thedesired Poised-realm state by adjusting this potential. This way, aquantum reservoir is realized that is not fully coherent, but has a verylong coherence time. Repeated measurements of this system reset itsquantum coherence, which decays very slowly. Thus, this system can bekept coherent for a sufficiently long time, so that superposition statesstay alive for the time intervals of single calculation steps.

The quantum degrees of freedom utilized in the reservoir may be anydegree of freedom that may be coupled between the nodes as well ascoupled to an input and output signal. Non-limiting examples of quantumdegrees of freedom include electronic excitation states, quantum spin(e.g., electron spin and nuclear spin), quantum angular momentum, andquantum linear momentum.

With reference to FIG. 8, a plurality of nodes 200 are contained withinor on a substrate 210. In some embodiments, the nodes 200 are fixed inor on the substrate. For example, a glass, silicon, or mica wafer may beused as a substrate 210 and the nodes 200 are adsorbed or deposited ontothe surface of the substrate 210. In other embodiments, the nodes 200are free to move within the substrate 210. For example, in someembodiments, the substrate 210 may include a liquid medium within whichthe nodes 200 are dispersed or dissolved. In some embodiments, the nodes200 are distributed in a regular array (such as by using establishedmicrofabrication techniques). In other embodiments, the nodes 200 arerandomly distributed.

In one non-limiting example, the nodes 200 are photosynthetic units thatare deposited on a mica substrate using adsorption from solution. Onesuch technique is described in Scheuring et al., The EMBO Journal (2004)23:4127-4133, which is incorporated herein by reference in its entirety.In this technique, cell membranes containing photosynthetic units fromRhodospirillum photometricum are dissolved into dodecylmaltosidesolution. The resulting extract is placed on freshly cleaved mica usingan adsorption buffer drop. The resulting structure includes a pluralityof photosynthetic units distributed across the surface of the mica.

The quantum reservoir described above may be used to build anon-algorithmic computational architecture based on the principles ofneural networks, such as echo state networks or liquid state machines.The general idea is (i) to drive a random, large, fixed quantumrecurrent neural network with an input signal, thereby inducing in eachnode within the reservoir to produce a nonlinear response signal, and(ii) produce a desired output signal by a trainable linear combinationof all of these response signals.

In some embodiments, the input signals comprise a quantum driving forcethat couple to one or more quantum degrees of freedom of the nodes 200.Non-limiting examples of suitable input signals include photons,electrons, and electrical or magnetic fields. In one embodiment, theinput signal is supplied to all nodes 200. For example, with referenceto FIG. 8, a laser 220 may send laser pulses 240 of appropriatefrequency to couple to a quantum degree of freedom in the nodes 200.

To translate a real-world classical input to the quantum mechanicalinput signal 240, an input processor module 250 may be provided. Thismodule comprises a traditional algorithmic computer, such as a generalpurpose computer, that receives a classical input signal 260 and drivesthe input signal generator (e.g., laser 220) based on the classicalinput signal 260. For example, a time-varying analog electrical signalmay be provided to the input processor module 250, which then translatesthat signal into appropriate time-varying driving of the signalgenerator 220. Thus, a time-varying classical input 260 results in atime-varying quantum input signal 240 being supplied to the nodes 200.For example, time-varying current or voltage may be provided to theinput processor module 250, which then drives laser 220 to produce acorresponding time-varying change in pulse frequency, light frequency,or intensity of laser light 240 being supplied to the nodes 200.

In response to the quantum stimulation and the quantum coupling of thenodes 200 to each other, nodes 200 may radiate out a quantum responsesignal, such as scattered photons. Each node 200 can radiate an outputsignal and that signal may radiate in multiple directions. Someembodiments provide a detector 270 that detects the time-varying outputsignals 280. In the case of scattered photons, the output signals may bedetected using photodetectors or a spectrometer. In some embodiments,the detector 270 includes an array of subdetectors in order to detectoutput signals 280 emitted in different directions. Other suitabledetectors may include a nuclear magnetic resonance detector or anelectron paramagnetic detector.

The result of the detection described above is a plurality oftime-varying output signals. The multiplicity of the signals may beprovided by detecting the time variation of a variety of parameters,such as the time variation of a plurality of frequencies of scatteredphotons or the time variation of photons scattered in a plurality ofdirections. The plurality of output signals may then be relayed to anoutput processor module 290. The output processor module 290 appliesweights or other signal processing algorithms to the plurality of outputsignals to produce a single output signal 300. This module comprises atraditional algorithmic computer, such as a general purpose computer,that receives the plurality of output signals from the detector 270 andcalculates the output signal 300.

The weights or other signal processing algorithm used to derive theoutput signal 300 from the plurality of outputs 280 produced by thenodes 200 may be determined using one or more training procedures, suchas is known in classical reservoir computing. One example of such atraining method is depicted by the flowchart in FIG. 9. At block 400, atime-varying input signal for which there is a known, desired output isprovided to the quantum reservoir as discussed above. At block 410, aplurality of time-varying output signals is received by a detector asdiscussed above. These signals as well as the desired final output aresent to the output processor module. The output processor moduledetermines a weighted combination or a set of weighted combinations ofthe plurality of output signals that will produce the desired finaloutput. In one embodiment, the weighted combination of outputs is alinear combination. In other embodiments, more complicated functionalforms are utilized. In some embodiments, the output processor moduledetermines the optimal functional form. Once a suitable combination isdetermined that produces the desired output, the corresponding weightsare stored in memory.

At block 440, it is determined whether there is any additional trainingdata (i.e., another known input-output combination). If so, theprocedure returns to block 400 for input of the additional data. Whenblock 420 is reached, the appropriate combination weights are determinedthat produces the desired output that is also consistent with allprevious training data. The new weights are updated into memory at block440. If no more training data is supplied, the procedure proceeds toblock 450, where a set of input data having no known output is suppliedto the quantum reservoir. The stored combination weights are applied tothe plurality of output signals in order to produce the final output.

In one non-limiting example, the above described quantum reservoircomputer may be implemented using a simulated spin system, such asprovided by D-WAVE. The commercially available D-WAVE computer containsa plurality of qubits consisting of superconducting currents thatsimulate spin. The inputs and outputs are electrical current. In itsintended mode of operation, the D-WAVE computer operates using onlyfully quantum coherent qubits and non-time-varying input (i.e., atraditional quantum computer approach). However, in the present context,all simulated spins, including those that are not fully quantum coherentare used as nodes for the quantum reservoir. Furthermore, a time-varyinginput signal and plurality of output signals is provided. With a properJ_(ij) and h_(i) set, the D-Wave Hamiltonian:

${{Hp} = {{\sum\limits_{i = 1}^{N}{h_{i}\sigma_{i}^{2}}} + {\sum\limits_{i,j}{J_{ij}\sigma_{i}^{2}\sigma_{j}^{2}}}}},$

can be guided through a finite size version of the metal-insulatortransition. At various low temperatures, the interplay of thermaldecoherence and the spectrum can be determined to achieve the propertiesnecessary for use as a quantum reservoir.

Trans-Turing Machine

In What Is Life, 1944, E. Schrodinger guessed that genes would be“solids” with quantum mechanical chemical bonds, and for our purposesnow, guessed that the gene would not be a periodic crystal, for thesewere “dull” but would be an aperiodic crystal that contained a microcodefor the organism. DNA is exactly such an aperiodic crystal. Themicrocode does not “describe” the generation of the organism or itsmaintenance, but accomplishes these by organized behaviors of matter andenergy coordinated by the “information” in the aperiodic crystal, plus,as it turns out, the entire cell as an open far from equilibriumthermodynamic system.

The information is “embodied” and culminates in building and maintainingan organism.

The embodied sense of information in Schrodinger's statement may becontrasted with Shannon and Kolmogorov information. The former consistsin the entropy of an ensemble of messages, in some finite alphabet, in aSource. The latter is the shortest program that will output a givensequence of symbols in a prestated alphabet. Both Shannon and Kolmogorovinformation measures tell us how much information we have, but not whatinformation “is.” All we have is syntax. Nor is there, by design, any“coming into being” of the information in question, nor any semantics ofthat information on Shannon or Kolmogorov. Thus, Shannon and Kolmogorovinformation is not embodied, is free of matter and energy, free ofspecific classical physics causal consequences that may be biologicallyfunctional in a cell or organism, and seems to float in the air, a thirdconstituent of the universe with matter and energy.

In contrast, Schrodinger's sense of the aperiodic crystal containing amicrocode for the organism has within it in an unarticulated way, theideas of the processes engendered by the microcode, (plus the cell as anopen thermodynamic system), hence the semantics of the code, that is,the specific processes, whether quantum, open quantum, poised realm, orclassical specific causal consequences, it engenders. More, matter andenergy are explicit in the processes engendered by the microcode.Information on a Schrodinger sense is embodied with matter and energy,not floating free as a third constituent of the universe.

The essential feature of the aperiodic crystal is broken symmetries, asin the DNA molecule with its essentially arbitrary sequence of bases, A,C, T, G along the aperiodic double helix.

Information in an aperiodic solid or any system combining quantum,classical and Poised Realm processes, is typically, but not always,embodied in the broken symmetries of the system. In particular, it isthe broken symmetries of the Hamiltonian of the classical, poised realmand the quantum systems with its classical physics borne Hamiltonianwhich may have many broken symmetries, which embody information,classical, Poised Realm, and quantum matter and energy, with a semanticsthat is the processes that are enabled by the constraints contained inthe Hamiltonians (or other constraints in the dynamics of the classical,Poised realm and quantum degrees of freedom). More these brokensymmetries constitute constraints on the release of energy. But “work”is the very constrained release of energy into a few degrees of freedom,(Atkins). Thus classically, this constrained release of energy is work,not heat or entropy. This information has a fundamental semantics inengendering processes that carry out thermodynamical work. Suchprocesses underlie any system capable of complex, diverse organizedbehavior built from a series of classical actions serving specificuseful purposes, however defined. (We turn to candidate definitions of“useful purpose”=“function”=“task” below.) The information or codeengendering such processes has an embodied meaning in this sense ofpurposeful (e.g. in terms of survival and reproductive success) systemsperforming classical actions, quantum and Poised Realm behaviors. A codehas to endogenously engender these classical actions (e.g., DNA), byconstraining the flow of matter and energy, to be embodied information.The reason we stress “classical behavior” is the fact that as quantum orPoised Realm quantum amplitudes propagate, nothing “real” happens in the“real classical world.”

The philosopher Immanuel Kant defined an organized being as that inwhich the parts exist (in the universe) for and by means of the whole,and the whole exists for and by means of the parts. A simple example isa collectively autocatalytic set of peptides, a concept invented in 1971by Kauffman ( ). Gonen Ashkenazi at Ben Gurion University in Beer ShebaIsrael has a nine peptide (small protein) collectively autocatalyticset. No peptide in the set catalyzes its own formation. Rather, eachpeptide catalyzes the formation of one or more other peptides among thenine peptides from fragments of those peptides. The nine peptide setachieves autocatalytic “catalytic closure” because all the nine peptideshave their formation from their fragments catalyzed by at least one ofthe nine peptides in the nine peptide set. Catalytic closure isprecisely an example of Kant's Organized being. The parts exist (in theuniverse) for and by means of the whole nine peptide autocatalytic set,and the whole collectively autocatalytic set exists for and by means ofthe parts. Call such a Kantian system, “Autonomous”. Given an autonomoussystem we can define the function of a part by the role it plays insustaining the existence of the whole in the universe. Note that theexplanatory arrows from upward from the parts to the whole, and downwardfrom the whole to the parts whose behaviors the whole organises.

Given an autonomous system a natural sense of purpose=function=task isgiven by those quantum, poised realm, and/or classical consequences ofthe parts that sustain the whole in existence in the universe. Note thatthe function of the heart is to pump blood, not make heart sounds orwiggle water in the pericardial sac. Similarly, the function of one ofthe nine peptides is to catalyse the appropriate reaction, not wigglewater in the medium. The function of a part is a subset of itsconsequences, only definable as above. Given the concept of autonomy, wecan see part of the reason Shannon and Kolmogorov information areinadequate if powerful. They are syntactic only, have no specific causalconsequences associated with the bits in the bit string, thus CAN haveno function in sustaining the autonomy of a system that gets to exist inthe universe. We will use autonomy with Trans-Turing systems below asone means to solve the famous Frame problem of computer science.

Thus, ultimately for the information to have effects in the decoherent“real world”, some variables of a quantum, Poised Realm, and/orclassical system must ultimately become classical.

The complex Hamiltonians available in Poised Realm Systems, open toquantum, Poised Realm and classical inputs and acting on their worldsvia quantum, Poised Realm and classical outputs, are constraints thatcan have many broken symmetries so contain a great amount of embodiedinformation enabling a high diversity of quantum, poised and classicalinformation processing and acting in the world of the system.

We show below that such a system is not a universal Turing Machine, nora classical “machine,” but much richer.

First we begin with a seminal paper by Dennis Salahub and coworkers,(JACS) that is a first major step toward Trans-Truing systems. de laLande, JACS (2011) 133:3883-3894, incorporated herein by reference inits entirety. Salahub et al. considered a simple system of many nucleiand electrons in two potential wells, (FIG. 6 in Salahub). Here the Xaxis is a reaction coordinate. The Y axis is energy. Two potentialwells, A and B lie in this plane, and overlap, the right hand ascendingbranch of the A well crosses the left hand ascending branch of the Bwell. The nuclei are at this crossing in the initial state, called the“seam region” and consist in a superposition of states, A and not A, Band not B. Nuclei are heavier than electrons, so, using a version of theLindblat operator, the nuclei decohere to classicity rapidly and,essentially at the same time, fall either into well A or well B. Theyhave passed from quantum superpositions to classical nuclei in one oftwo displaced potential wells. The immediate consequence is that theelectron cloud responds DIFFERENTLY according to whether the nuclei havedecohered to well A or to well B. Thus, as we claim in general forTrans-Turing Systems, as some quantum degrees of freedom decohere toclassicity, (or are measured), that ALTERS the behavior of the remainingquantum degrees of freedom. This is an essential step towardTrans-Turing systems.

Note next that in a slightly more refined model, the many nuclei woulddecohere to classicality in some temporal order and, say, spatialrelation. The result is that the now increasing number of classicalnuclei will have an ever changing classical Hamiltonian as additionalnuclei become classical and interact with one another dynamically,ignoring or not the electron cloud. Thus in a Trans-Turing system, asquantum degrees of freedom decohere to classiciality, or are measured,the classical Hamiltonian changes and exhibits NON-Random Behavior. Butthat non random behavior IS the classical system itself behaving underthe ever changing Hamiltonian, which may move the system on the X axis.In turn, as a generalization of the fact that decoherence into well Aversus well B alters the effects of the nuclei on the electron cloud,the behavior of the many nuclei in possible temporally alteringbehavior, non-randomly alters the effects on the quantum degrees offreedom. Then in the Poised Realm, some of the quantum degrees offreedom can be in superposition states, hence exhibit constructive anddestructive interference. By our discussion above, high amplitudes, oramplitudes with high energy and moduli, preferentially decohere. Or, ifquantum measured, by the Fermi Golden rule, high amplitudespreferentially are measured. In either case, the altered quantumbehavior via constructive and destructive interference and by the Bornrule for pure or mixed states, has the consequences that non-randomchanges are made in which quantum degrees of freedom decohere or aremeasured and become classical in the next short time interval. In turnthis again alters the classical Hamtonian via the newly classicaldegrees of freedom, which again alters the quantum and Poised Realmdegrees of freedom hence which amplitudes decohere to classical behavioror are measured to classical behavior preferentially next. Conversely,REcoherence of classical degrees of freedom, without limitation bydriving with a laser light, alters which classical degrees of freedombecome quantum, thereby altering non-randomly the classical Hamiltonianand altering non-randomly the consequent poised realm open quantumbehaviors and quantum behaviors of the Trans-Turing system.

The above is the heart of a Trans-Turing System. Its behavior is NOTdeterminant, for either by superposition and constructive anddestructive interference plus decoherence preferentially of highamplitude modes with large moduli, or their preferential measurement viathe Golden rule, the system is non-determinate. Thus the Trans-Turingsystem is not algorithmic. But it is also, in its global behavior,non-random. So the behavior is not standard closed quantum systemquantum random as in the Schrodinger equation and von Neumannaxiomatization of quantum mechanics. The Trans-Turing system is entirelynew.

In one embodiment, there are six criteria for a system to exhibitTrans-Turing behavior. First, the system contains quantum degrees offreedom propagating in short lived superposition states that decayrapidly due to decoherence. But these short lived superposition statesundergo constructive and destructive interference and will be one basisfor a NON-Determinacy in the Trans-Turing system when coupled todecoherence to classicality for all practical purposes, FAPP, or quantummeasurement.

Second, either via decoherence or motion out the X axis or both, quantumdegrees of freedom become classical FAPP or via quantum measurement,become classical “Simpliciter”. Both decoherence and measurement areacausal and yield the non-determinant behavior of the Trans-TuringSystem.

Third, there are, in addition, coupled classical degrees of freedom inthe TTS.

Fourth, when quantum degrees of freedom, and either superposition statesor pure states become classical FAPP, or are measured, that ALTERS indifferent specific ways the effects of the now classical degrees offreedom on one another, thus alters the non-random collective dynamicsof the coupled classical degrees of freedom. In turn this alterednon-random classical behavior alters non-randomly the behavior ofremaining quantum degrees of freedom.

Fifth, in turn this non-random alteration of the behavior of theremaining quantum degrees of freedom alters non-randomly which of theopen quantum degrees of freedom decohere or move out the X axis toclassicality FAPP. In particular, higher quantum amplitudes tend todecohere with higher probability. So non-randomly altered quantumbehavior, including altered constructive and destructive interference,alters non-randomly which amplitudes become higher, thus altersnon-randomly which amplitudes decohere to classicality FAPP.

Sixth, in turn, classical FAPP degrees of freedom can recohere, forexample, driven by a coherent electromagnetic field whose intensity andperiod distribution can be tuned non-randomly thereby injectinginformation. The recoherent degrees may achieve a new controlledsuperposition state, thereby altering non-randomly the constructive,destructive, and pure states behaviors among themselves and otherquantum amplitudes, thereby non-randomly affecting which amplitudesachieve higher amplitudes and tend to decohere, and also non-randomlyaltering the behaviors of the coupled classical degrees of freedom inthe TTS.

Evolution itself indicates that Trans-Turing systems are fully feasible.Mutations in evolving organisms can be quantum indeterminate. Yetevolution in the 11 fold evolution of the eye, the convergence ofoctopus and human camera eye, the convergent evolution of marsupials andmammals seen in the Tasmanian wolf and mammalian wolf, the streamlinedforms of the porpoise and shark, all say evolution by natural selectionis strongly NON RANDOM. Thus, the twin pillars of XX century physics,quantum mechanics with its von Neumann measurement Born rule randomness,and Newton's and Einstein's classical physics, literally demonstratesthat the evolution of the biosphere itself is not determinate, hence notalgorithmic, but not random. So too, the Trans-Turing System. At last wecan move beyond the classical physics, algorithmic, Turing machine.

Trans-Turing Information Processing and Acting by Poised Realm Systems.

A Universal Turing Machine consists of an infinite tape a finitealphabet of discrete symbols written on discrete squares on the tape, afinite set of discrete states in a reading head. At each instant, thehead is located over one square on the tape. It responds to the symbolon the tape and its internal state by staying in place, moving onesquare to the left, or one square to the right. It then, depending uponthe symbol it read, and its internal state, erases the symbol on thetape below it and writes a symbol, changes from its internal state toone of its internal states, and iterates. All digital algorithms in allcomputers are based on the Universal Turing Machine.

A critical feature of the Universal Turing Machine is its absolutedefiniteness. Given an input symbol and a state at a position of thereading head on the tape, the entire future behavior of the system isdefinitely determined. Despite the famous halting problem, known in theart, the system is algorithmic, definite and an abstraction of a perfectmechanical classical machine.

A second class of computers are classical analogue computers, where, forexample, electric circuits mimic the water flow in a system of pipes.These systems are entirely classical if also sometimes chaotic. They mayexhibit epistemological indeterminism in that we do not know the initialstate with infinite accuracy, but not the ontological indeterminsm ofquantum mechanics, the Poised Realm, and Trans-turing systems viadecoherence to classicality or quantum measurement of open quantum andPoised realm systems.

It will be clear to those of ordinary skill in the art, that the PoisedRealm Systems in described here are neither universal Turing machines,nor classical variable analogue computers. Rather Poised Realm Systemsutilize quantum, Poised Realm, and classical degrees of freedom, alongwith exogenous quantum, Poised Realm, and classical inputs and outputsfrom and to the environment. The quantum degrees of freedom in thePoised Realm are not limited in any way to quantum COHERENT qubitrealizations of Universal Turing Algorithmic Machines as in conventionalquantum computers. Rather the quantum degrees of freedom create simpleor complex quantum wave patterns, standing or propagating, and, in thePoised Realm, exhibit both superpositions and a finite number ofamplitudes with finite positive moduli which can become classicaldegrees of freedom by decoherence or measurement and can recohere toquantum behaviors, pure or superposition states.

Constructive and destructive interference occurs among the quantumdegrees of freedom whether fully coherent, or Poised Realm amplitudes.As described, the sensitivity to decoherence increases with the energyof an amplitude of one or many single or entangled quantum degrees offreedom. In short quantum and Poised Realm amplitude wave crests ofamplitudes peak and are likely to decohere to become classical degreesof freedom.

As used herein, the phrase “bright idea” refers to quantum waves whoseamplitude moduli are sufficiently great that they have a highprobability of decohering to classical degrees of freedom, andthereafter modifying the Hamiltonians governing the classical andquantum behaviors of the system.

The consequence of one bright idea decohering to classicity andmodifying the Hamiltonians of the quantum, Poised Realm, and classicalsystem, together with the quantum, Poised Realm and classical inputs tothe system, will be a succession of bright ideas and modifications ofthe classical and quantum Hamiltonians of the Poised Realm system. Thisdynamics is neither quantum nor classical, neither determinate, hencenot algorithmic, nor random. The Hamiltonian keeps changing as quantumor Poised Realm degrees of freedom become classical and classical onesbecome Poised Realm or quantum coherent.

These changes in the Hamiltonians can move the Poised Realm system onthe x-axis from order to criticality to chaos and back, by its ownendogenous dynamics and as driven by quantum Poised Realm, or classicalinputs. Or alternatively, alteration in the quantum network structure ofcomponents of the system can move it on the x-axis either from quantumPoised Realm behavior to classical behavior without movement on they-axis, or with movement on the y-axis as sensitivity to decoherence andrecoherence stimuli and noise change.

We discuss next entanglement among quantum and poised realm degrees offreedom and how the behaviors of those degrees of freedom can becorrelated with the “outside world” via the, in general, shapedpotential wells, created by the classical degrees of freedom of thesystem. First quantum entanglement and nonlocal EPR correlations arefully established. We propose use of fixed or SHIFTING patterns ofentanglement among quantum and poised realm quantum degrees of freedomin one or a SET OF INTERACTING AND COUPLED TRANS-TURING SYSTEMS. Suchentanglement may be achieved by any means known or discovered in theart, including infrared photon couplings among generalized chromophoreswithin one or a set of Trans-Turing systems. Entanglement means that thequantum degrees of freedom are a SINGLE CORRELATED SYSTEM. Hence, withquantum measurement, the measured quantum degrees of freedom of theentangled quantum degrees of freedom ARE correlated and violate Bell'sinequalities. Recent results demonstrate that the more degrees offreedom are entangled the GREATER IS THE CORRELATION, in dramaticopposition to the familiar curse of dimensionality in classical physics.Thus either measurement of a plurality of entangled poised realm orquantum degrees of freedom yields a HIGHLY CORRELATED SET OF NOWCLASSICAL DEGREES OF FREEDOM ENABLING COORDINATED ACTION BY THETRANS-TURING SYSTEM INVOLVING MANY, NOW CLASSICAL, DEGREES OF FREEDOMCOUPLED TO ONE ANOTHER AND STABLY CLASSICAL DEGREES OF FREEDOM WITHINTHE TRANS-TURING SYSTEM.

As is know in the art, study of random Boolean networks, RBN, andthreshold networks demonstrate a classical physics order, criticalitychaos transition. The discrete analogue of the Lyapunov exponent, calledthe Derrida Curve, shows convergent flow in the ordered regime, neitherconvergence nor divergence at criticality, and divergent flow in thechaotic regime. We believe the same results hold true for Hamiltoniansystems of many nonlinearly coupled variables on the X axis. It is ofdeep importance that critical RBN show maximum diversity in theirbehavior as measured by SET COMPLEXITY, ( ), a power law distribution of“avalanches of dynamical change” when a single variable is transientlyaltered, which allows maximum controlled communication across a networkof many variables without tipping into uncontrollable chaos where anynoise discoordinates behaviors, yet maximizes useful discrimination ofpast events. Critical classical systems are optimal with respect to thecapacity to classify environments and act reliably in the presence ofnoise. We propose that single or man coupled CRITICAL Trans-Turingsystems, including coupled by entanglement, will allow, afterdecoherence to classicality or measurement, wide correlation among manynow classical degrees of freedom. But more, because these systems arecritical with respect to classical behaviors, the richest, most diverse,and coordinated actions and discriminations can occur in such systems.

Further, in the Poised Realm, critical systems exhibit fractalamplitudes which, we believe, for a multiparticle system, may also allowmaximal Poised Realm coordination of, for example and withoutlimitation, entangled quantum and Poised Realm degrees of freedom in oneor a plurality of coupled Trans-Turing systems.

Because critical PoisedRealm systems resist decoherence best via powerlaw decoherence rather than exponential, they should, by the FermiGolden rule, or preferential decoherence of high modulus amplitudes,tend to transfer quantum energy to classical energy efficiently.

Consider a classical particle in a box. If we measure its position andmomentum we know nothing of the shape of the box! But a quantum waveprocess in a potential well “knows” in an analogue embodied sense, theboundary conditions constituted by the potential well. This may show up,without limitation, in the eigen values of its energy levels. Thusquantum wave processes, and Poised Realm quantum wave processes in aclassical potential, know the “CONTEXT” OF THAT POTENTIAL.

Now consider the contrast of a digital representation of music in a roomby dividing the room into tiny volumes and using a bit series torepresent the music, versus a set of 1000 differently shaped drum headswell placed in the room, so “tuned” to sense the music in the room bytheir joint patterns of vibration, ie the eigenfunction modes of thedrum heads. But the drum heads are not coupled. Now consider a pluralityof entangled quantum or poised realm degrees of freedom which decohereto classicality or are measured. They ARE ONE quantum state, they “know”their classical potential surface context. Now, if that surface is tunedto reflect and span the outside world in some more or less organizedway, the measured or decoherent hence now classical degrees of freedom“know the “outside world”.

The next step is to realize that the decoherence to classicality ormeasurement process, in reflecting the classical Hamiltonian of theclassical degrees of freedom is both the TUNING OF THE QUANTUM WAVEFUNCTIONS to the world outside, like the drum heads, but also theMeasurement” bias provided by the classical Hamiltonian of the system asa “measuring instrument. The resulting classical degree of freedom of asingle or many entangled degrees of freedom is “the answer”, as is apointer reading in a standard quantum measurement. We will use thisbelow to attempt to solve the Frame problem in algorithmic Turingsystems.

It will be clear to those of ordinary skill in the art, that movement ofthe Poised Realm System only on the x-axis altering the quantum networkstructure, or in any other way noted above or more generally, can resultin quantum, and quantum Poised Realm degrees of freedom becoming more orentirely classical, thereby altering the quantum network and furthermodifying the position of the Poised Realm system on the x-axis, and bybecoming classical, these degrees of freedom can also alter theHamiltonians of the classical, quantum and Poised Realm degrees offreedom, again inducing motion on the x-axis by endogenous or inputdriven signals.

Because of quantum, Poised Realm and classical outputs of the system tothe environment, actions will be taken by the Poised Realm system on itsworld, by virtue of the Poised Realm system and the quantum, PoisedRealm, and classical input “information” it receives. Thus, the PoisedRealm system is an embodied, non-Turing, non-determinate,non-algorithmic, non classical non-random analogue, informationprocessing and acting system that embodies information “analysis,”action, and information within the Poised Realm System enabled by thesymmetries and broken symmetries of its Hamiltonians, classical andquantum, quantum network structure and driving by quantum or PoisedRealm inputs which may move the system on the x and y axes. The brokensymmetries of the Hamiltonians can constitute the “tuning” of thequantum “drum heads” if tuned by coupling to the outside world, in oneor a plurality of Trans-Turing systems.

Because the classical variables of the Poised Realm system may beendERGONIC or exogONIC processes, these may, in general, be linked intowork cycles. Poised realm systems can “build things” by being capable ofcarrying out thermodynamical work in the context described above.

Design and Evolutionary Selection of Desirable Poised Realm Systems.

Consider first the simulation by digital computers with algorithms, ofPoised Realm systems with desired inputs and with outputs. One use ofsuch algorithms is to design Poised Realm systems with input outputbehaviors that are desired, in rough parallel to the fully computerizeddesign process of the 777 Boeing jet. A second broad application of suchalgorithms is in any of the many evolutionary selective algorithms thatoperate on a given algorithmic representation of the behavior of aPoised Realm system, and makes any kind of use of any kind of “heritablevariations” and selection of the behaviors of such Poised Realm systemsto achieve input/output and internal behaviors that are desired. Forexample, on rugged fitness landscapes, “long jumps” by big mutations arepreferable when fitness is low, but local variations are more effectivewhen fitness is high, in speeding evolution and avoiding trapping onpoor local optimal. Genetic Algorithms are just one such evolutionaryalgorithm known in the art. But algorithmic Turing simulations cannotconstitute the real behavior of a Trans-Turing system, for Turingsystems are classical physics and Trans-Turing Systems are not.

A broad second way to design or evolve desired Poised Realm systems useswithout limitation, liposome vesicles with chemical reactions, andchemical constituents in its interior and exterior milieu. Withreference to FIG. 10, liposomes contain phospholipid molecules 700 thatorganize into a bilayer that forms a vesicle with aqueous regions on theinside and outside of the bilayer. Included herein are both unilamelarand multilamelar vesicles. In a Trans-Turing system, the vesiclescomprise chromophores 710, including generalized chromophores definedabove, in the broad sense (e.g., including chromophores coupled to oneanother) by binding to beta barrels or other bilipid spanning moleculesin the liposome membrane so that the chromophores are inside, or outsideor both, of the liposomes and can communicate by broadcast or morespecifically with one another, quantum, Poised Realm and classicalinputs. The quantum and poised realm degrees of freedom within oneliposome or a plurality of liposomes constituting a Trans-Turing systemor plurality of such systems may or may not be entangled, as describedabove. The vesicles can be divided in any way to daughter vesicles withor without replenishment of chemical constituents, and selected fordesired Poised Realm behaviors as embodied physical systems. Suchsystems are both embodied, not representational as are Turing systems,achieve functional closure as autonomous systems, and thus are notsimulated on an algorithmic computer, but are embodied systems thatexist and behave in the universe.

Generally, to form liposomes with proteins embedded in the bilipid layera further classical approach is to isolate the protein of interest(generally overexpressed) from living cells, by destroying the cellintegrity. Integral membrane proteins are associated to membranes whichare broken during the cell distruction but reseal to form lipid vesicles(containing membrane proteins) or membrane fragments.

At this point these membranes (containing proteins) are solubilized withexcess detergent and sometimes a synthetic lipid (e.g. POPC) to formmixed micelles (detergent+cell lipids+POPC+membrane proteins). In eachconcrete case, it is routine to find the best detergent for solubilizingthe protein without destabilizing its 3D structure and interaction withvery proximal lipids. Typical examples are sodium cholate, andoctyl-glucoside, digitonin, dodecyl maltoside, and Triton-X-100.

Now the detergent can be removed by dialysis or gel filtrationchromatography or adsorption on biobeads or simply by dilution.Detergent is preferentially removed due to its higher solubility inwater. The product are lipid vesicles (possibly containing some celllipids) containing the protein of interest. The typical size is 50-100nm. But the presence of the protein can affect the size. Theseintegral-protein—containing liposomes are called “proteoliposomes”. Theprocedure to prepare liposomes in this way is called “detergentdepletion method”.

At first approximation, proteins are oriented 50% inward and 50%outward, so for every vectorial application, 50% of protein is notactive.

Further discussion of liposome manufacturing techniques suitable to makethe structures described herein may be found in Silvius, J. R. (1992)Solubilization and Functional Reconstitution of Biomembrane Components.Annu. Rev. Biophys. Biomol. Struct. 21, 323-348 and J.-L. Rigaud, B.Pitard, D. Levy. Reconstitution of membrane proteins into liposomes:application to energy-transducing membrane proteins. Biochimica etBiophysica Acta 1231 (1995) 223-246, both of which may be incorporatedherein by reference in its entirety. Examples are described in: GoodwinMg, Jackson Jb, Electrochromic Responses Of Carotenoid Absorbency BandsIn Purified Light-Harvesting Complexes From Rhodobacter-CapsulatusReconstituted Into Liposomes, Biochimica Et Biophysica Acta Volume: 1144Issue: 2 Pages: 191-198 Published: Sep. 13, 1993; Jackson Jb, GoodwinMg, Electrochromic Responses Of Bacteriochlorophyll Absorbency Bands InPurified Light-Harvesting Complexes Of Rhodobacter-CapsulatusReconstituted Into Liposomes, Biochimica Et Biophysica Acta Volume: 1144Issue: 2 Pages: 199-203 Published: Sep. 13, 1993; and Kobayashi M,Fujioka Y, Mori T, Terashima M, Suzuki H, Shimada Y, Saito T, Wang Z Y,Nozawa T, Reconstitution of photosynthetic reaction centers and coreantenna-reaction center complexes in liposomes and their thermalstability, Bioscience Biotechnology And Biochemistry Volume: 69 Issue: 6Pages: 1130-1136 Published: June 2005; all of which are incorporatedherein by reference in their entirety.

In order to make giant liposome vesicles, GVs, the vesicles produced asabove are dried over an electrode and after application of alternatecurrent, GVs are formed, and they contain the integral membrane proteinin the membrane. This is a variant of the “electroswelling method”. SeePhilippe Girard, Jacques Pécréaux, Guillaume Lenoir, Pierre Falson,Jean-Louis Rigaud, Patricia Bassereau, A New Method for theReconstitution of Membrane Proteins into Giant Unilamellar Vesicles,Biophysical Journal—1 Jul. 2004 (Vol. 87, Issue 1, pp. 419-429), whichis incorporated herein by reference in its entirety. Alternatively, theproteoliposomes formed after detergent depletion can be lyophylized andhydrated without stirring. This corresponds to a sort of “naturalswelling” method that should give protein-containing giant vesicles.

Liposomes can bud as is known in the art. By budding in the presence offree and covalently anchored chromophores linked thereby to betabarrelproteins in the aqueous medium or other similar molecules, thesechromophores will melt into the membrane and become anchored there. Thusthe density per liposome of chromophores, and their spectralcharacteristics can be altered. Since coupling of two chromophoresdepends upon emission of a quantum by one chromophore whose size can beabsorbed by the second, tuning the chromophore absorption spectra andratios in a liposome partially controls the topology of the quantumnetwork, hence position of the liposome system on the x-axis.

Here, rather than using a genetic algorithm of any kind REAL EVOLUTIONof embodied liposomes coupled or not, or any other embodied systemscapable of any kind of reproduction, division, heritable variation andselection after Darwin, can be used to evolve desired input,Trans-Turing “computation” and output behaviors, quantum, Poised Realm,and classical.

It will be clear to one of ordinary skill in the art that one preferredembodiment of the current invention is able to evolve a population ofsingle or interacting Trans-Turing systems to achieve with more or lesssuccess, a high diversity of success criteria or figures of merit. Ingeneral, one approach to this is to use any one or combination of thewide variety of known in the art methods for evolution of such devices.The Holland Genetic Algorithm and its many variants are but one set ofexamples.

In the broadest terms, the inputs to a Trans-Turing system can be anysingle or combination of coherent quantum behaviors, poised realmbehaviors, or classical behaviors of single or many degrees of freedom.The outputs can similarly be any one or a plurality of quantum coherent,poised realm or classical degrees of freedom. In general, only classicaldegrees of freedom, including quantum measured degrees of freedomwithout their being a limiting example, can serve as readily sampledoutputs.

In general, the inputs to the quantum system will be transformed intothe outputs of the Trans-Turing system. The Trans-turing system, may,like a feed forward neural net, have no internal dynamical attractorsincluding potential wells, or it may have potential wells of theclassical variables which are capable of such behavior, withoutlimitation, because they typically can exhibit dissipative dynamics.These alternative attractors, including without limit, potential wells,can be used to classify diverse inputs, including those which areconstant in time, into the different attractors of the classicalvariables of the Trans-turing system, where which attractor is attainedfor some period of time depends in general on the initial state of theTrans-Turing system as well as its inputs.

As an entirely non-limiting example of such input-output andclassification by a Trans-Turing system achieved by any form ofevolutionary search, we consider a Trans-turing system consisting of asingle liposome containing chlorophyll and surrounding antenna proteins.As a non-limiting example, the antenna protein or any other moleculelike it, will float in the liposome lipid bilayer. In general, raftingwill occur bringing the diverse chlorophyll and antenna proteins intoproximity, for example without limitation by van der Waals forces. Ingeneral any such molecule has a longer axis. Without limitation, use redand green quantum dots or fluorescent dyes to label the two defined“head” and “tail” ends of the long axis of such a molecule aschlorophyll wrapped by the antenna protein.

Then by any means known in the art, the orientation of any two or morelabeled chlorophyll and antenna proteins in the lipid bilayer can easilybe assessed by standard techniques. Thus, it will be clear to those ofordinary skill in the art, that for a plurality of two or more red andgreen labeled molecules, here, without limitation, taken to bechlorophyll molecules each wrapped by its labeled red and green antennaprotein, the relative orientations and distances among these moleculesfloating in the liposome membrane can be assessed. These classicaldegrees of freedom, without limitation, ca be taken as one possible outof indefinitely many, classical “output variables”.

We note that the success criterion, or “figure of merit” may be a steadystate of our output variables or any time varying dynamical behaviors,and the input variables may be steady states, time varying states,stationary statistical distributions or non-stationary distributions.Here we consider the simplest case of steady inputs and their mapping tosteady outputs.

Without limitation, we take as a concrete example of input variables twolasers with different wavelengths that shine on the single liposome. Theintensity ratio and wavelengths of these laser lights can be taken as aninput “spectrum”. For N input laser frequencies there is an Ndimensional input space.

As a second classical variable input set we take sound vibrations at twoor more frequencies in which the ratio of the power intensities of thedifferent frequencies, and those frequencies themselves can be changedto cover an N dimensional input space for N input frequencies.

For either the quantum laser, or classical sound vibration inputspectrum, for each point in the N dimensional input space, the relativeorientations and distances of the red and green labeled, withoutlimitation, chlorophyll and antenna protein complexes can be asses bylight scattering, image analysis or any other means includingmathematical analysis of the orientations and distances among the outputred and green labeled molecules which may raft together to variousdegrees in the bilipid layer.

A mapping from input space to the output variables whose relativepositions constitute an output space can now be established.

Without limitation, it may be desired to achieve a Trans-turing systemthat maps each point in the input space to a unique point, bijectively,in the output space. Alternatively it may be desired to “classify”subsets of the input space to the SAME output point in the output space.In general this classification can arise if the Trans-Turing system hasattractors such as a plurality of two or more potential wells that areexpressed in two different stable or statistically discriminablebehaviors of the output variables.

To achieve such a one to one bijective mapping, or a many to oneclassification of the input space to the output space, a diversity ofevolutionary algorithms may be carried out.

Without limitation, let the Trans-turing systems above be liposomes withcontrollable densities of chlorophyll and antenna proteins dissolved inthe bilipid layer, with additional classical control parameters such asthe hypertonicity or hypotonicity of the medium leading to swelling orshrinking of the liposome, to a diversity of lipids altering thephysical-chemical characteristics of the liposome bilipid layer andhence the rafting and other behaviors of the chlorophyll and antennaproteins floating in the bilipid membrane, hence their collectivebehaviors under van der wal and other forces. Other classical inputs canbe electric and magnetic fields, temperature, pressure, and so forth.

Call these variables, which can be classical, quantum coherent, orpoised realm, the CONTROL PARAMETER SPACE. An evolutionary search inthis “control parameter space” is undertaken by varieties ofevolutionary algorithms, below, to “hill climb” to points in the controlspace that optimize the desired input output behavior of theTrans-turing systems to obtain at least one or a plurality ofTrans-Turing systems that performs as optimally as is attainable giventhe complexity of the search space and ruggedness of the resulting“fitness landscape” ie the distribution of the desired behavior or“figure of merit” across the Control Parameter Space. As is well knownin the art, the success of evolutionary search by variations alone orwith any analogue of recombination, depends upon the ruggedness of the“fitness landscape” for the “figure of merit”. In general, forms ofrecombination perform poorly on quite or very rugged landscapes. Also,when fitness is low, larger variations in Control space parametersfollowed by smaller variations as fitness increases, can optimizeevolutionary search. In addition, the very process of evolutionarysearch can be used to establish the statistical features of the fitnesslandscape as is known in the art.

Using these parameters, let an initial population of, withoutlimitation, 1000 liposome Trans-turing systems be constructed and testedindividually for their input output mapping, where the initial figure ofmerit of each liposome Trans-turing system is established and correlatedto the positions of each in the Control Parameter space.

Again, without limitation, one or some plurality of the fittest liposomeTrans-Turing systems are used as seeds for a second generation ofliposomes. To be concrete, let, without limitation, the 100 fittestliposomes be used as this seed. Then construct from each of these 9 newliposomes differing from it at defined distances in the ControlParameter space, with the distances tuned to the current fitness and theruggedness of the landscape as it becomes established. This creates asecond generation of liposome Trans turing systems, here without anyform of recombination.

Iterate the above and assess the figure of merit for the new secondgeneration of liposome Trans-Turing systems, again pick the 100 best,and form a new 1000 liposome third generation. Iterate this process asmany times as desired, as fitness increases.

This is the core of an evolutionary search process, here using liposomesas Trans-Turing systems, and so far without any analogue ofrecombination.

Recombination can be implemented by taking two or a plurality of membersof the chosen seed set, here 100 liposomes, and forming the newgeneration by considering the Euclidian or, for discrete ControlParameters in the control parameter space, the Normalized CompressionDistance, between any two or any pair of more than two members of theseed set. New points can be chosen at any distance from any one liposometoward any other single or set of liposomes in the control parameterspace, by simple means known in the art. This is a kind of “sharing ofinformation” among the seed set to form the next generation forevolutionary search. In general, too much sharing is unfavorable on arugged multipeaked landscape where it may cause trapping of all on poorlocal optima. Thus as the structure of the landscape is discovered usingmeans known in the art, by the evolutionary sampling process itself, thepreferred ratio of mere variation and “generalized recombination or“sharing” can be tuned to optimally search the landscape.

By these means, for any input space, output space and figure of merit,Trans-turing systems well adapted to any single figure of merit can beattained.

More generally, there may be more than a single figure of merit, wherethe relative importance of the different figures of merit are unknown.Here the standard solution concept is “Global Pareto Optimality”, iepoints in the Control Parameter Space where no motion can occur thatincreases ONE figure of merit without lowering one or more other figuresof merit. Among such Pareto optimal points, the global pareto optimalset is such that no other Pareto optimal points are “better” on any ofthe figures of merit that the Global Pareto Optmal Points. In general,each figure of merit creates its own smooth or rugged fitness landscape,and the search for global pareto optimal points can be difficult, but ingeneral is possible. A theorem proves that among the Global Paretooptimal points, each global optima of any one of the figure of meritfitness landscapes is one of the Global Pareto optimal points. Thus iffinding a global optimum of a single figure of merit is feasible or eveneasy on smooth landscapes, finding some Global Pareto Optimal points isreadily achieved.

It will be clear to those of ordinary skill in the art, that theseevolutionary search processes can be used for any form of Trans-turingsystem, whether liposomes, nanofabricated with nanotubes or constructedin any other ways.

The same evolutionary search processes generalize to a plurality of twoor more Trans-Turing systems which are coupled in any way, classically,by entanglement, or in other ways of coupling quantum coherent degreesof freedom or poised realm degrees of freedom. To use our concreteexample of an output space generalized to M liposomes, there is now anN×M input space and an N×M output space, and an N×M Control Parameterspace for N control parameters per trans-turing system. The sameevolutionary procedures apply, with the figure of merit able to be farmore complex because it now involves possible steady state and for anysingle Trans-Turing system or plurality of them, complex classical,poised realm and quantum coherent behaviors.

Quantum dots, as known in the art, absorb and emit photons. Large dotsabsorb in the red, small dots in the blue. So smaller dot sizes changesthe absorption spectrum toward shorter wave lengths. Quantum dots have anumber of higher excited states emitting, by Fermi's Golden Rule,preferentially their largest quanta as they fall from their higherenergy states to their ground states. This can allow quantum dots ofdifferent sizes to be coupled by photon exchanges in liposomes or moregenerally in any setting including nano-fabrication in Trans-Turingsystems.

Similarly, quite subcritical chromophore coupled systems with smalltrees will absorb and emit photons that are shorter wavelength thanlarger trees closer on the x-axis to critical. These absorption spectracan be tested. The distribution of tree sizes in a liposome or on ananodevice will tune the overall connectivity of the entire system,hence position on the x-axis. Again, the presence of multiple energylevels per quantum tree of various tree sizes can allow the trees tocommunicate by emitted and absorbed photons in a tunable way.

For liposomes, exposure to hypotonic and hypertonic solutions will swellor shrink the liposome altering the proximity of chromophores hencetheir photon mediated connectivity, hence position on the x-axis.Swollen liposomes will be further left on the x-axis than the sameliposome if shrunk in a hypertonic solution.

In one nonlimiting preferred mode of evolution of Poised Realm systems,the liposome contains an autocatalytic set of polymers and catalyststhat catalyze a sequence of chemical reactions to create the buildingblocks of the polymers Recent work by Serra has shown that under theseconditions, autocatalytic set and liposome division SYNCRHONIZE,enabling the open ended evolution demonstrated by Szathmary et al. insilico. This is a generalization of Ashkenazi's nine peptideautocatalytic set, now experimentally achieved. We will call suchsystems Poised Realm Protocells, subject to heritable variation. Naturalselection and even co-evolution of such systems in defined or variableenvironments can be carried out to achieve Poised Realm protocells withdesired input, output and internal behaviors. More, such systems willinteract not only by catalysis, but by myriad classical causal featuresenabling Darwinian preadaptations and the emergence of novel functions,as discussed by Kauffman in his books Investigations and Reinventing theSacred. Because these systems, like evolution in general, marry quantum,poised realm, and classical degrees of freedom, and are autonomousKantian systems with top down and bottom up causality, they escape merereductionism, and can show emergent behaviors. For example swim bladdersin some fish with a tunable ratio of air and water allow neutralbuoyancy in the water column. Paleontologists believe that these aroseas unused causal consequences of the lungs of lung fish as Darwinianpreadaptations, or exaptations. In Reinventing the Sacred Kauffman showsthat we cannot prestate the state space of the evolving biosphere, hencefurther we cannot know the boundary conditions on selection, so wecannot have entailing law. But more, the swim bladder, which arose dueto selection in a population of fish for good function AS A SWIMBLADDER, HAD THE FURTHER PROPERTY THAT, ONCE IT EXISTED, IT CONSTITUTEDAN ADJACENT POSSIBLE EMPTY NICHE. A bacterium might evolve only able tolive in swim bladders, like a bacterium only able to live in the lungsof sheep. BUT NOTE THAT NO SELECTION AT ALL ACTED TO CREATE THE SWIMBLADDER AS A NEW ADJACENT POSSIBLE EMPTY NICHE! The new empty adjacentpossible niche, “just arose”. But this means something astonishing: thebiosphere is literally building, without selection, the verypossibilities it will become.

In an exactly parallel fashion, evolving and convolving Trans-TuringProtocells can and will undergo Darwinian preadaptations and create“emergent” adjacent possible empty niches for more such Trans-TuringProtocells. By these means, and those below, the frame problem of Turingmachines and computer science can be solved: novel functionalities andsolutions to problems can be found under appropriate selectiveconditions.

It will be clear to those of ordinary skill in the art, that anyplatform, beyond liposomes, that can hold “generalized chromophores” ina changing or fixed spatial arrangement, can be used. In particular, ifthese can grow and divide spontaneously or non-spontaneously, and in anyform undergo “heritable variations” needed for evolution or even openended evolution, populations of Poised Realm Systems that can beselected for desired behaviors can be obtained and evolved.

In addition to Trans-Turing protocells that can evolve, this inventioncan be used in another way to evolve single or coupled Trans-Turingsystems for desired behaviors. Specifically, Trans-Turing systems can benanofabricated or micro or macrofabricated. An evolutionary procedurecan be carried out by an embodied version of something like the Geneticalgorithm, but, because embodied, beyond it. Here a population of aplurality of single or coupled Trans-Turing systems, without loss ofgenerality, nanofabricated ones, can be tested for a desired behavior.The best one or a subset of the initial population can then be used in avariety of ways to construct a second generation which might include thebest one or plurality of the first generation, and small mutant variantsof these Trans-Turing systems. Over a succession of generations, as theevolve and by interacting with one another, co-evolve, improveperformance can be sought. Because these systems are embodied and havereal Poised realm and classical consequences in the physical world, theyevolve in it without digitally representing that world, as in Turingmachines and the Holland Genetic algorithm. Thus, the famous andunsolved “frame problem” which bedevils Turing systems, does not evenarise for these embodied systems, for they evolve without digitally oralgorithmically representing their worlds.

By use of direct design, the use of digital algorithms both to simulateand evolve in silico, as described above, or nanofabrication of embodiedTrans-Turing systems, alone or coupled sets of them, nanotechnology candesign/evolve and co-evolve and build Poised Realm devices withdesirable properties, including input and output behaviors that aretrans-Turing in their information processing. Such systems are notalgorithmic in the Turing sense, nor classical physics analoguecomputers which at most have epistemological indeterminism viadeterministic chaos, while Trans-Turing systems have ontologicalnon-determinism, yet analyze input quantum, Poised Realm, and classicaldata, have “bright ideas” that become classical degrees of freedom,alter Hamiltonians or quantum network topology, hence position on thex-axis by endogenous dynamics and due to quantum, Poised Realm, andclassical inputs, yield a sequence of bright ideas and sequences of dataanalyses and quantum, Poised Realm, and classical actions on the worldby the embodied information processing, hence SEMANTIC system. In oneembodiment of this invention, Trans-Turing Protocells are KantianOrganized Systems and achieve Kepa Ruiz Mirazo's “autonomy” such thatthe parts exist in the universe for and by means of the whole, and thewhole exists in the universe for and by means of the parts whosebehaviors it organizes. We call these “Autonomous Trans-Turing systems”.They will be of use in affording a natural definition below of R.Ashby's “Essential Variables” as an internal goal state of aTrans-Turing system or coupled set of Trans-Turing systems.

It will be clear now, that such novel systems exhibit dynamics that areneither Schrodinger closed system quantum mechanical, nor classicaldeterministic dynamics. THE SYSTEMS ARE NEITHER DETERMINISTIC, hence arenon-algorithmic, and are NOT random. These Poised Realm Trans-Turingsystems exhibit novel dynamics allowing entirely novel informationprocessing, internal behaviors, and output behaviors among quantum,Poised Realm, and classical degrees of freedom.

Embodied Poised Realm Systems can Form Communicating and ActingNetworks.

Poised realm systems, without loss of generality, liposomes ornanotechnology devices, or otherwise, can form arbitrary networks inwhich quantum or Poised Realm, or classical degrees of freedom can becommunicated between Poised Realm systems such that they interact as a“community”. Coupling can be by any means known in the art, includingbroadcast, waveguides directing photons emitted by one Poised Realmsystem and directed to one or a plurality of other Poised Realm systems,use of quantum wires, fiber optic cables, carbon nanotubes or any othermeans of communication. As noted above the quantum and Poised Realmdegrees of freedom may be quantum entangled. More, recent work showsthat such an entangled system can alter which degrees of freedom areentangled. Because quantum measurement or decoherence to classicalityconstitutes the formation of correlated sets of now classical variablesvia that entanglement, and the pattern of entanglement can change, wecan think of this as a kind of “shifting of attention” by theTrans-Turing system or coupled set of Trans-turing systems. After theentangled degrees of freedom shift, a different set of quantum or poisedrealm variables become classical with consequences for the coordinatedbehaviors of the classical and Poised realm aspects of the system.

By such communication, communities of Poised Realm Systems can performtasks and information processing and acting that no single Poised Realmsystem can attain.

More co-evolution and other “adaptive procedures” or community assemblyprocedures, analogous to community assembly in ecology, can be used toobtain Poised Realm communities with desired properties. Among these maybe a maximal power efficiency per unit “fuel” or energy input to thePoised Realm devices, at a finite displacement from equilibrium. Recentresults suggest that bacteria grow at a rate that maximizes biomassproduction per unit fuel, here glucose, as input to the system. Thispicks a specific displacement from thermodynamic equilibrium as optimalwith respect to power efficiency per unit fuel for such systems. We heregeneralize this to Poised Realm systems performing any kinds of taskswith optimum power efficiency per unit fuel.

Ecologists suspect a similar maximum power efficiency for ecosystems. Wecan evolve communities of Poised Realm systems to maximize a powerefficiency per unit “input,” energy, or information as described below,or both or more general success criteria.

As noted above, Critical Trans-Turing systems and either preferentialdecoherence of high amplitudes to classical degrees of freedom orquantum measurement and Fermi's Golden rule, coupled with the mere powerlaw decoherence of Critical poised realm systems, implies that maximumpower transfer from quantum to classical degrees of freedom can beobtained. Maximum power efficiency may be attainable.

Using Essential Variables to Enable Goal Behavior.

In Design for a Brain by Ross Ashby, 1960s, Ashby designed aself-repairing algorithmic system, the homeostat. He considers a systemof N variables, discrete variables and discrete time. He designates asubset, E<N, of these as “Essential Variables,” each of which must bekept with “bounds” given the range of values of each variables. Callthis bounded region the “Alive Box.” The system must keep within theAlive Box. Note that in an Kantian Autonomous system that gets to existin the universe, the means of parts and the whole by which theAutonomous system sustains itself constitutes its Essential variables.

The N variables comprise a dynamical system with state cycle dynamicalattractors and basins of attractions draining into each state cycle asis known in the art. See Kauffman's Origin of Order as a nonlimitingexample.

The system is released from an initial state, flows to an attractor andeither does or does not keep within the Alive Box. If yes, the systemremains in that attractor of the N variables. If not, it reinitiates ata random state in the state space and flows to an attractor. Again ifthe system stays within the Alive Box, it remains in that attractor, ifnot the process is iterated.

If the system fails to remain in the Alive box after some number ofrandom initial states, Ashby implements a “step change” in a parameterto one of the variables. This step change can change the “phase spaceportrait” of where the basins of attraction and attractors are located.

Again, the system is released from random initial states and if itremains for one of these in the Alive Box, the system stops. Otherwiseafter a number of initial states have been sampled, a step parameter isagain changed. The process is iterated until a value of the parametersis found that allows at least one attractor of the N variable system tokeep within the Alive Box.

These ideas are fully applicable to Poised Realm systems. A subset ofthe classical variables are designated as essential variables.

In continuous nonlinear dynamical systems with attractors andparameters, at a bifurcation point in parameter space, new attractor(s)may appear, old ones disappear, and the locations of basins ofattraction draining continuous trajectories into attractors may change.

In a Poised Realm System, the decoherence on the y-axis, or motion onthe x-axis, of a quantum degree of freedom to a classical degree offreedom can operate on the Hamiltonian, or quantum network structure ofthe classical and quantum systems as a parametric bifurcation parameter.Indeed, continuous variation on the y-axis from quantum to classical canact as a bifurcation parameter as do motions on the x-axis or both the Xand Y axes. In addition, quantum or classical parameters can be changed.The recoherence of a classical degree of freedom, or motion toward orderon the x-axis, can act as a bifurcation parameter to the classical andquantum Hamiltonians. In addition, inputs, classical or quantum, maydrive the system between attractors or drive the system so rapidly thatattractors are not attained and maintained. However, the average timespent in the Alive Box is always definable.

To create a Poised Realm System “homeostat” we carry out the processesnoted above. The Poised Realm system keeps changing by decoherence orrecoherence of quantum or classical degrees of freedom, or changes inclassical or quantum parameters, or changes in inputs, until the systemmaintains itself in the Alive Box.

This architecture endows the Poised realm system with “primary drives”,i.e., to keep within the Alive Box.

Choosing Essential Variables.

As noted above, choosing essential variables is not trivial. In PoisedRealm evolving protocells, examples of Kantian autonomous Trans-Turingprotocells, autonomy itself that maintains the Kantian organized beingin the universe, alone or in the presence of natural selection forevolving protocells picks the relevant essential variables and theirembodied classical causal consequences that form a functional closure oftasks by which the Kantian system sustains itself. These are thevariables whose change increases “fitness” by whatever success criteriais in operation.

Note that for embodied Trans-Turing protocells as autonomous systems,adaptation and preadaptations using existing causal features of theclassical variables for novel functionalities, or “tasks” that achieve“task” closure in a set of tasks (like a dividing eukaryote), solves theframe problem. Again, the system does NOT represent its world digitally.It exists and evolves as an embodied Trans-Turing System or a coupledplurality of them, perhaps as a population that evolves or co-evolves,in an environment. New functions and tasks achieved by new “uses” ofcausal features of the classical variables, enabled also by the PoisedRealm and other Trans-Turing features of the system, promote adaptation.Selection for desired behaviors is then carried out, as in biology.

For an evolving population of mutated budding liposomes or generationsof mutant liposomes where the ratio and density of chromophores withdifferent absorption/emission spectra are varied, hence varying quantumnetwork connectivity and position on the x-axis, those variables whichstrongly alter fitness for the desired goal are good candidates foressential variables. The same is true for an evolving population ofnanotech devices with similar mutations in chromophore, carbon nanotubestructures and specra, and topologies of connections. Those variationswhich strongly affect fitness for the desired goal are good candidatesfor essential variables.

Secondary Goals.

Biology teaches us that evolution can achieve tasks via a sequence ofevolved subtasks. Ontogeny is a prime example. It will be clear that theembodied Trans-Turing system protocell Autonomous system(s), in anenvironment with inputs, classical and quantum, and outputs acting onthe world, classical and quantum, may attain states and Hamiltonianswhich can serve as subgoals. Here, the Essential Variables may or maynot be kept within the Alive Box, but a different, perhaps overlappingset of sub-essential variables are kept within their own bounds,Secondary Alive Box. From the Secondary Alive Box, the Poised RealmSystem can attain the Alive Box by some variety of “simple” steps.Without limitation, a simple “step” is to initiate the Poised RealmSystem in a quantum, Poised Realm, and classical state which is nearthat which attains the Secondary Alive Box, and from this state, thesystem flows, with or without decoherence and recoherence of quantum,Poised Realm, and classical variables that change the classical andquantum Hamiltonian, readily to the Alive Box sustaining configurationof the system.

A partial ordering or hierarchy of Secondary and Tertiary Alive Boxconfigurations of the Poised Realm system can sometimes be found, withaccess via these partial orderings or hierarchial orderings to theconfiguration of the Poised Realm system such that it remains in theAlive Box. The partial ordering leads from a single or more generality aplurality of Nth level Alive boxes to one or a plurality of N−1 or lowerlevel N−2,3, alive boxes.

Beyond Autonomous Trans-Turing systems undergoing embodied evolution,there is a second means of perhaps much more rapid non-biological“learning” of adaptive behavior, goals and subgoals that solves theframe problem. As a non-limiting example, subdivide the EssentialVariable Alive box into successively smaller subspaces that contain oneanother, labeled 1, 2, 3, 4, 5 meaning “getting better, 1->5” This is ananalogue of an emotional human response to solving a problem where eventhe “form” of the solution is unknown hence beyond solutionalgorithmically due to the frame problem. Now, we have seen that highamplitudes with high energy and moduli preferentially decohere, and havecalled them “bright ideas”. Decoherence or measurement typically leadsto decoherence or measurement of high moduli amplitudes. In turn thisleads to a slight modification of the classical Hamiltonian and resultsin a change in the Hamiltonian of the quantum system. A succession ofmeasurements or decoherence events leads to a succession of “brightideas” becoming classical, so a succession of modifications of theclassical Hamiltonian and Hamiltonian of the quantum system. Think ofthese decoherence events, or measurement events carried out by theclassical degrees of freedom on the quantum degrees of freedom in somebasis that the classical degrees of freedom constitute as “asking aquestion” and getting a classical variable answer in a single, orentangled set of open quantum or Poised Realm variables when someasured. The results of the now classical variables may be to move thesystem from box 1 in the Alive box toward Box 2, then 3, then finally 5.Call being in the 5 box A Solution. Then the system has gone through asuccession of measurement or decoherence questions, a sequence ofclassical variable answers, until it finds a solution that keeps thesystem in the “happy” box 5. At that point, the system either stopschanging as in Ashby's case, or uses the relevant classical variables asa memory store for the solution given the problem. In order to adapt todifferent problems in different “environments”, the system may need to“ignore” the memory classical variables. This may be possible byrendering them quantum or poised realm again via recoherence. As quantumdegrees of freedom again, they cannot affect the behaviors of theclassical degrees of freedom of the system. The details remain to beworked out.

Operant Conditioning of Poised Realm Systems.

Given the Alive Box and a diversity of Secondary and Tertiary and higherorder Alive Boxes, the Poised Realm system needs memory classicaldegrees of freedom. As noted above, such memory degrees of freedom canarise by decoherence of quantum degrees of freedom where these degreesof freedom can remain classical indefinitely. Or they can becomeclassical by measurement and remain classical including by the quantumzeno effect. Or they can become classical by motion on the x-axis. Oncememory variables exist, they serve as bifurcation parameters in theclassical Hamiltonian of the total system.

These Memory classical variables maintain aspects of the classical,Poised Realm, and quantum Hamiltonians of the total Poised Realm systemsuch that the Alive box and subboxes can be attained and sustained.

Given such Memory variables, the Poised Realm System can undergo“operant conditioning”. Given some input to the system, it attains asubgoal Alive box from which it can attain the Alive Box. In the subgoalbox, memory classical variables arise by decoherence on the Y, motion onthe x-axis or both X and Y axes, so classical parameters change, and thesystem attains the Alive box. Given the classical state of the nowclassical memory variables, the system responds to the inputs from theworld by attaining either the subgoal box, or directly the Alive box.

Given the Alive Box and decoherence or motion on the x-axis, of quantumvariables to classical Memory variables which can remain classical forlong periods of time, as well as classical variables which can becomepartially or completely quantum, both of which change the Hamiltonian'sof the quantum and classical systems, hence their dynamical behavior,the Alive Box serves as “internal motivation” as in Ashby's Homeostat,and the Poised Realm system will search on its own means to use anyinput stream of quantum or classical data, its own internal quantum andclassical Poised Realm dynamics, and its outputs—which it may “observe”,for example via sensors, the Poised Realm System will search and oftenattain a state that takes the input stream and with or without subgoalboxes, old or new, achieve a state that remains in the Alive Box. Thus,the Poised Realm System has “learned” to map some aspects of the inputdata stream to specific internal structures and dynamics, including thememory variables, and learned at the same time to map the inputs touseful outputs that keep the Poised system in the Alive Box.

More on Attention in the Poised Realm System.

By virtue of the classical Hamiltonian, or any other classical system,without limitation, a nonlinear dynamical system capable of order,criticality and chaos, as evidenced by work on Random Boolean networks,Piecewise linear networks, linear ODE networks, and Threshold Tanhfunction networks, and the possible entangled (and possibly measuredentangled) correlated quantum behavior in the Poised Realm, the systemwith quantum, Poised Realm, and classical inputs may “focus attention”on any subset of its input stream, internal state—which it may sense bysensor degrees of freedom—and output behavior—which again it may sense.Thus the Poised Realm system need not be effected by all inputs, quantumor otherwise. Or that effect may be very minimal, so that the system“sees” and “responds” to focused aspects of its inputs, internal states,and outputs. Again we note that shifting patterns of entanglement, as isknown in the art, allow sequential shifting of the focus of attention.

By “focusing attention” on any subset of inputs, and carrying out bothdata processing and actions coupled to that input, the total behaviorcan become relevant, without limitation, to keeping the system in theAlive Box. Thus, the system can “notice” features of its environment andactions, and modify its behavior to keep subgoals attained, or remainwithin the Alive Box.

There is an analogy between a quantum degree of freedom becomingclassical for some period of time and the “step changes in parameters”advocated by R. Ashby in his “Design for a Brain” to change the systemsuch that essential variables are kept within bounds. In addition, thereis a similarity between the changes in the Hamiltonian of a Poised Realmsystem, when some of its quantum degrees of freedom become classical,and the preparation of a quantum system plus is classical components ina quantum experiment by measurements that make quantum degrees offreedom classical in the prepared quantum system. In effect, thispreparation step can be thought of as reshaping the classical andquantum Hamiltonians of the prepared system thereby picking a favoredpointer basis.

This has a bearing on quantum computation where the quantum algorithmcan be thought of as reshaping the Hamiltonian of the quantum system,which then accumulates high modulus amplitudes in the vicinity of thesolution so that von Neumann consistent measurement is likely to givethe “right answer” after a number of measurements. Thus, the spontaneousdynamics of a Poised Realm system where, given the current Hamiltoniansof the classical and quantum system, some amplitudes can “peak” to highmoduli and remain quantum or can decohere preferentially to classical“answers” to a “question” posed by the current Hamiltonians. Thus, suchPoised Realm systems appear to be non-algorithmic quantum-PoisedRealm-classical computing and “doing” systems.

In a general sense, what we here call a change in the Hamiltonian of aquantum and/or classical system when a quantum degree of freedomdecoheres to classicity for all practical purposes is similar to theBorn-Oppenheimer approximation for “effective Hamiltonians” due to slowand fast changing variables such as nuclear positions and electron clouddistributions in molecules. Note that Salahub et al used thisapproximation in their paper, as described above.

The Diversity of Organized Behaviors of Poised Realm Systems.

Kauffman introduced Random Boolean networks as models of geneticregulatory networks in 1967 and 1969 (see Reinventng the Sacred, by S.Kauffman Oxford UP 1993, 1995, 2000 and Basic Books 2008). Thesesystems, and continuous cousins including piecewise linear equations byL. Glass, linear code systems by S. Thurner, and nonlinear thresholdnetworks by M. Andrecut and Kauffman, show that such systems behave inan ordered regime, a chaotic regime and an “edge of chaos” criticalphase transition.

Critical networks exhibit remarkable features, ranging from maximumstorage of information (Shmulevich), maximum pairwise mutual information(Ribeiro et al.), maximum Set Complexity, explained further below (Galaset al.), maximum power efficiency (Carteret et al.), maximum capacity toevolve gracefully (Aldana et al.), maximum capacity to make reliablediscriminations of past events and reliable action in the presence ofminor noise, and maximum capacity in a “society” of networks that caninfluence one another to create novel attractor behaviors in the membersof the society or “tissue” or “colony” (Damiana et al.).

Galas et al. have introduced a new measure of the diversity of organizedprocesses a classical causal system can carry out, called setcomplexity. Consider a random binary string, e.g., (10100010).Concatenate this string with itself, (1010001010100010). Now use acompressor such as gzip to compress the concatenated string. Since theconcatenated random string is redundant, and of length, here N=8, forthe initial string, the compressor will reduce the concatenated stringlength 2×N, to length N by eliminating redundancy. Now take twodifferent random strings length N, and concatenate them and try tocompress them. They cannot be compressed, so remain length 2N.Normalized Compression Distance is a universal distance measure betweenobjects such as binary strings. The extent to which two strings,concatenated, can be compressed is a measure of the similarity betweenthe strings. That similarity is a distance measure, and is normalized bydividing by N.

Set Complexity is a new measure for such objects. Let there be M such,without loss of generality, binary strings of length N. Calculate thepairwise normalized compression distance for all distinct pairs ofstrings and normalize by the number of pairs to find the averagenormalized compression distance among M strings. Call this average, E.Set Complexity is defined as SC=E×(1−E). This measure is 0 if E=0 or 1and reaches a maximum for E=0.5.

The intuition behind set complexity is that M identical binary stringsmust have low set complexity, and also M strings that are random withrespect to one another must have low set complexity. Thus set complexityreaches a maximum for intermediate values of E. It is a new measure ofthe diversity of objects, or, if the symbols represent actions byvariables, e.g., the output values of N variables in a random Booleannet, it represents the diversity of organized processes of theclassically causal systems.

It is exciting that critical Random Boolean Nets sharply maximize SetComplexity defined over the M states on all state cycles of the network.In short, the asymptotic behavior of critical random Boolean netsmaximizes the organized diversity of processes such systems can carryout.

We extend this definition of set complexity to Poised Realm Systems.With respect to the classical variables of the system, the SetComplexity definition is identical. Using the discussion by W. H. Zurek,Decoherence and the Transition from Quantum to Classical-Revisited, LosAlamos Science No. 27, 2002, we extend set complexity to the quantumdegrees of freedom of a Poised Realm system. The mutual information, I,between two quantum systems, S1 and S2 is I(S1,S2)=H(S1)+H(S2)−H(S1,S2).Without loss of generality, the entropy, H, in the above formulation canbe taken as the von Neumann entropy as is known in the art.

Using this measure of mutual information I, we compute the mutualinformation between, without loss of generality, two quantum or PoisedRealm degrees of freedom, S1 and S2. Then, for a set of quantum andPoised Realm quantum degrees of freedom in a Poised realm system, wecompute the mean mutual information, E, between all pairs of quantumdegree of freedom ion the Poised Realm System where E is normalized to amaximum value of 1.0. Quantum Set Complexity is then E×(1−E).

We define the total classical and quantum set complexity as SetComplexity (classical)+Set Complexity (quantum). Classical systemsbehaving as described by Hamiltonians can be quantized. Not allclassical causal systems are so describable by a Hamiltonian, forexample, random Boolean nets. However, the x-axis for our kicked quantumrotor, or a kicked quantum oscillator goes from order, with 0 Lyapunovexponent, to a second order (critical) phase transition, to chaos forclassical Hamiltonian systems. We believe that the Set Complexity forHamiltonian systems is maximized for critical classical Hamiltoniansystems whether by motion on the y-axis, the x-axis or both. We alsobelieve that total set complexity for a Poised Realm System is maximizedfor critical classical and critical quantum and Poised Realm quantum andclassical behaviors. If so, such Poised systems, classical and quantumcan carry out the greatest diversity of organized processes hence areoptimal for many practical applications.

More generally, total set complexity is maximized for Poised systemswith inputs and outputs somewhere in the Poised Realm, and can beobtained for optimal task performance.

Using the above, we have a design criterion for Poised Realm systemscapable of carrying out the maximal information processing, internallydiverse dynamical Poised Realm behaviors, and the richest Poised Realmactions on the world or in communities of Poised Realm systems.

It may be that Poised Realm systems can simultaneously maximize a powerefficiency per unit fuel, in a generalized sense of fuel as energy, andthe diversity of organized behaviors as in the Set Complexity measuresabove, by operating along the critical line in the Poised Realm. Orthere may be a more complex trade off between maximum power efficiencyand displacement from equilibrium and maximum set complexity. Both areopen to utilization in single Poised Realm Systems or communities ofPoised Realm systems.

Possible neurobiological implications: i. We propose that in thevertebrate brain and even in Box Jellyfish, Trans-Turing behavior occursin molecules, probably within synapses, perhaps in neurotransmitterreceptors. We propose that experience, qualia, are associated withquantum measurement. We propose that entangled degrees of freedom ineven anatomically unconnected synapses enables a Unity of Consciousnessto solve the binding problem of neurobiology, we propose that theclassical behaviors of neurons and sensory tunes tiny time-spacevariations of transmembrane potentials that constitute the classicalHamiltonians that “tune the drumhead potentials” to cover the externalworld when measurement occurs, we propose and answer to Descartes: Themind acts acausally on the brain either by decohence or measurement, andcan do so repeatedly via recohrence or flowering of quantum behaviorsafter measurement.

Based on this, one conclusion is that molecules, probably in synapses,comprise evolved Trans-Turing systems. Then we propose that neuralnetworks of real neurons, coupled with modes of mechano-sensory or otherinputs, can be molded to be potentially conscious systems capable ofpractical non-algorithmic problem solving including solving the frameproblem and unity of consciousness.

Two approaches to test this are: i. See if neurotransmitter receptorscan carry out quantum measurement and test of anesthetics freeze them ina classical state such that they cannot measure, so qualia cannot arise.ii. Select for ease of ether anesthetization in some organism, sayDrosophila melanogaster, until little or no ether is needed to produceanesthetization. Compare wild type and mutant proteins for quantummeasurement. The wild type should be able to carry out quantummeasurement, the mutant proteins should not be able to carry outmeasurement, or able to do so to a so to a reduced extent perhaps bybeing frozen classical.

In a preferred embodiment of Trans-Turing systems we make use ofincorporation of, without limitation, chlorophyll molecules and theirantenna proteins, or other molecules into liposomes, (1-4). Here thechlorophyll and antenna proteins may be embedded in the membrane of theliposome and move in the membrane surface. Alternatively the chlorophylland antenna proteins may be affixed to one or more macromolecularassemblies, or by means known in the art to artificial nanostructuressuch as, without limitation, nanotube structures, and affixed at knownpositions and orientations to such nanostructures, for example usingstreptavidin and biotin.

Work on chloroplasts of diverse light harvesting organisms shows thatthe average intermolecular distance between chlorophyll-antenna proteincomplexes ranges from 10 to 20 angstroms. Coherent energy transfer byquantum coherence ranges up to 100 nM, (5). These figures set an initialestimate for the density of chlorophyll antenna complexes that must beincorporated into a liposome of known surface area and volume, typicallyon the order of 1 micron or less in diameter, to achieve the desiredaverage distances between chlorophyll antenna complexes in the liposomewhere these complexes float. By means known in the art, rafting of suchantenna protein complexes as they aggregate in the liposome membrane canbe used, by means known in the art, to achieve higher densities in localsubregions of the liposome complex's surface membrane.

An established means known in the art to create liposomes containing aknown and tunable mean density of chlorophyll antenna complexes is basedon a process in which chloroplast membranes are dissolved in a detergentlike sodium deoxycholate along with phospholipid. The detergent isremoved by dialysis, the lipid reassembles into lipid vesicles, and theproteins and chlorophyll are incorporated into the bilayers. One cancontrol the ratio of chlorophyll to surface area simply by varying theamount of lipid in the mixture. If one wishes, one can purify thereaction centers ahead of time from a photosynthetic membranes.References to these procedures are incorporated by reference below,(1-4).

In an alternative preferred mode of realization of Trans-Turing systems,noted above, the chlorophyll antenna protein complexes or othermolecules are affixed to a nanotube two or three dimensional structureof desired structure and affixed to this using biotin and streptavadinby means known in the art to specific locations on the nanotubestructure. The latter structure with affixed chlorophyll and antennaprotein complexes are then incorporated into liposomes by dissolvinglipids, without limitation, phosopholipids, or any other lipids capablefor forming liposomes, in medium containing the nanostructure withaffixed chlorophyll and antenna complexes. The latter structures areincorporated into at least some of the newly formed liposomes, creatingTrans Turing systems.

Alternatively nanotube or other nanostructures with chlorophyll andantenna proteins, or any other molecules, afixed eg by streptavadin andbiotin, may be used to create a Trans-Turing system withoutencorporation into a liposome or other bounding membrane or structure.

The Trans-Turing systems so constructed can exhibit quantum coherentbehavior in electron transfer among antenna protein chloroplasts,including entanglement (5). In addition, one must calculate all possiblequantum pathways from antenna chloroplast A to B. Those pathways thatpass through the medium, or “bath” in the interior of the liposome caninduce decoherence, (5). Thus these systems also live in thequantum-classical poised realm. By means of incident driving quantum orclassical input, for example, and without limitation, laser light oftuned wavelength and intensity, recoherence can be induced. Thus thesesystems can hover in the poised realm. As noted above, by tuning therandom versus periodic features of the driving stimulus, the degree andrate of decoherence and recoherence can be controlled.

In addition coupled quantum systems, can exhibit open quantum coherentto decoherence to classicality to recoherence without incident laserlight, Ali Nissim, (pc).

As is known in the art, Sholes Included by reference, (5,6),Two-Dimensiopnal photon echo (2DPE) spectropscopy has recently emergedas a practical method for detailed insight into excited state dynamics.Information in 2DPE spectra includes the TIME EVOLUTION of decoherenceof coherent superpositions of the absorption bands, which provides ameasure of quantum coherence.

It will be clear that 2DPE spectropscopy can be used throughout thispatent application for all cases requiring measurement of power lawversus exponential decay of decoherence to measure criticality (powerlaw decoherence) or ordered or chaotic position, (exponentialdecoherence) on the X axis. This is true for measurements of moleculeswithin Trans-Turing systems as they behave, hence we can measuredecoherence and recoherence in a Trans turing system or set of coupledTrans-Turing systems. As noted above in this patent application,deviation away from criticality in the Poised Realm yields mix forms ofdecoherence between power law and exponentials themselves with variousdecay rates, that can be used to measure position on the X axis ofmolecules in Trans-Turing systems, in situ, or not, and for drug designas noted above. Thus we can study and follow poised realm behaviors ofmolecules in time in Trans-Turing Systems, and in cells with respect todrug action, and in neural synapses, which may constitute Trans Turingsystems, whose molecules, including neurotransmitters and theirreceptors may be in the poised realm and play a role in conscious andunconscious mental behaviors along with quantum measurement events inquantum coherent or poised realm systems.

We note that spin echo (7) and neutron spin echo (8) can also be used tomeasure decoherence.

More, we note that new means are known in the art to achieve controlledentanglement of quantum degrees of freedom, (9), hence entanglement canplay a role within and between molecules in one or a plurality oftrans-Turing systems, including possibly Trans-Turing behaviors in oneor more anatomically connected or unconnected neural synapses. Byquantum measurement of one or a plurality of entangled degrees offreedom in Trans Turing Systems, where the degree ofEinstein-Podolsky-Rosen NON LOCAL quantum correlations increase with thenumber of entangled degrees of freedom, highly correlated behaviors ofmeasured, hence now classical, degrees of freedom within one, or aplurality of molecules in a single or set of Trans-Turing Systems,including possible a set of anatomically unconnected but entangledmolecules in neural synapses, can arise. These correlated now classicaldegrees of freedom can have classical causal consequences for the totalsingle or set of coupled trans-turing systems and their quantum, poisedrealm, and classical behaviors.

The above Trans-Turing systems have classical, quantum coherent, andpoised realm inputs, and outputs, including from and to other nearbyTrans-Turing systems, thereby forming a “society” of interactingTrans-Turing systems. Without loss of generality, entanglement among thequantum degrees of freedom in one or a plurality of trans-turing systemscan occur and can be altered, thereby altering which measured, and nowclassical degrees of freedom are highly correlated to act jointly asclassical aspects of the Trans-Turing system on the Trans-Turing systemwith respect to its quantum coherent, Poised Realm, and classicaldegrees of freedom and act as classical aspects of the outputs of theTrans-Turing system.

As noted above, the total behavior of Trans-Turing systems is notdefinite, via decoherence to classicality FAPP, or quantum measurementof coherent or poised realm behaviors, yet not random due to classicaldegrees of freedom and their classical Hamiltonian, plus the changingeffects of the changing classical behaviors on the quantum coherent andPoised Realm behaviors.

It will be clear to those of ordinary skill in the art, given ourspecifications above, that we can obtain organic molecules in general,or other molecules, calculate their position of the Xorder-criticality-chaos axis using the graph theoretical techniquesnoted above, test for their position on the X axis, and in particularfor Poised Realm Critical behavior by testing for power law decoherenceat criticality in the Poised Realm, compared to a gradual conversion toexponential decoherence with different exponential decay rates asmolecules are located on the X axis further toward order or chaos fromcriticality. Thus, we can assemble, in general, molecules of any desireddistribution on the X axis, from all critical, to any otherdistribution, for incorporation into liposomes to create Trans-Turingsystems.

Alternatively we can use such molecules in the X axis on nanofabricatedTrans-Turing systems. Or we can use macroscopic Trans-Turing systems.

In a preferred embodiment of this invention, the molecules incorporatedinto the liposome to create trans-turing systems will be closelyclustered around the critical location in the Poised Realm. Here weexpect a maximum of controllable behavior as the quantum chaotic domainsdescribed above increase in size up to merging, or not quite merging,into the giant component described above at Poised Realm criticality. Weexpect the most complex Poised Realm behavior here, at theconductor-insulator transition critical transition described above. Morewe expect the most complex computational behavior among critical coupledclassical degrees of freedom, and we expect optimal energy transfer fromquantum modes to classical modes of behavior at criticality based, asnoted elsewhere on Fermi's golden rule of preferential measurement ofthose amplitudes with the highest modulus, or preferential decoherenceof amplitudes with large moduli. The energy will be released into thenow classical degree(s) of freedom.

Using our graph theoretical calculations, we can synthesize, or screenfor by use of combinatorial chemistry means known in the art, moleculesof any sort, eg without limitation, binding a known ligand, orcatalyzing a known reaction, or binding to a stable analogue of atransition state, at known positions of the X axis for incorporationinto Trans-Turing systems, for the behavior of molecules in Trans-Turingsystems alone or coupled, or drug candidates. As we noted above, thefailure of classical physics—“lock-key” ideas for combinatorialchemistry, where Kauffman has the founding international patents filedin 1985, to yield functional drugs, compared to the success in Japanesepharmaceutical companies which continue to use medicinal chemistrytechniques, suggests that the medicinal chemistry techniques may wellbe, inadvertantly, probing in vivo Poised Realm behaviors, beyondclassical lock-key concepts, in drug discovery. This bears on our usesof the Poised Realm for drug discovery as described above.

Link to Consciousness in the Human Brain, and coupled Trans-TuringSystems.

The human brain has about 10 to the 11 neurons, each with an average of600 synapses. Each axon ends on one dendrite. Many dendrites, each withmany synapses, feed into one downstream neuronal cell. With the arrivalof an action potential at a synapse, neurotransmitter molecules arereleased, travel across the synaptic cleft and bind to neurotransmitterreceptors. Often this results, via a complex of molecules including thereceptor, in opening or closing a channel on the post synaptic dendrite,leading to tiny time/space alterations in the local transmembranepotential. These alterations travel to the axon hillock of the neuralcell and are summed. If the transmembrane potential increases to lessthan about −20 mV, an action potential is likely to be initiated andtravel down the axon to impinge on one or more downstream synapses.

Francis Crick, in the Astonishing Hypothesis, (10), points out that avast amount of information is thrown away concerning the behaviors ofvastly many molecules in synapses and tiny time space alterations indendritic transmembrane potentials to achieve either firing or notfiring of a classical physics action potential.

We believe it is a sensible hypothesis to “stand the brain on its head”,and ask whether the synapses are the “business end” of the brain, whosebehavior is partially driven by the sensory inputs and classical physicsneural network among the 10 to the 11th neurons and 600 times as manysynapses. If so, the synapse itself may be a Trans-Turing systemoperating in the Poised Realm, where decoherence, recoherence, andquantum measurements may occur.

We hypothesize that conscious experience is associated with quantummeasurement in coherent or poised realm quantum systems. The resultingclassical degrees of freedom, post measurement, allow the conscious mindvia these classical variables to have classical physical consequencesfor the total mind-brain system, answering Descartes about how mind actson matter. Measurement is NOT causal, so mind does not act causally onmatter. In addition, decoherence to classicality FAPP may allow mind tohave acausal consequences for brain.

The hypothesis that conscious experience, qualia, are associated withquantum measurement is testable in two ways at least: i. anestheticsbind to neurotransmitter receptors in hydrophobic pockets. If the“freeze” neurotransmitters into classical or classical FAPP behaviorsuch that the neurotransmitters receptors cannot undergo measurementevents, while in the absence of anesthetics neurotransmitter receptorsdo undergo measurement events, that is evidence that consciousexperience, ie “qualia”, IS associated with quantum measurement. Inaddition, fruit flies, Drosophila melaogaster, can be etheranesthetized. Selection of anesthetization with decreasing ether dosescan yield mutant proteins that, with anesthesia for little or no ether,may reveal by standard genetics the protein and other moleculesassociated with consciousness. Then the mutant proteins or othermolecules can be tested for “freezing” such that they cannot undergomeasurement, while the unselected normal, or wild type versions of thoseproteins can undergo quantum measurement. These experiments can helpidentify the possibly synaptic molecules whose quantum and Poised Realmand classical behavior is related to consciousness. On this view,decoherence to classicality FAPP may be associated with unconsciousactions of mind on brain.

If these results are obtained, we can construct living neural networksof controlled network “architecture” and dendritic synapticinterconnections, graft these to sensor inputs, say, without limitation,from the Box jelly fish eye and its downstream neurons as inputs to theabove neural net, and effector neurons acting on artificial outputdevices, limbs, actuators and so forth. From these neural systems, orusing non-neural general Trans-Turing systems alone or coupled,including coupled by entanglement, we can create devices that classifytheir worlds, solve the frame problem, and act on their worlds, see justbelow “Evolving Trans-Turing Systems.”

More, by entanglement of diverse unconnected or connected quantumdegrees of freedom in diverse synapses, or trans-turing systems, andquantum measurement of those entangled degrees of freedom, highlycorrelated, due to Einstein Podolski Rosen non local “EPR” quantumeffects violating Bell's inequalities will arise, and the now highlycorrelated and also now classical degrees of freedom can be used to actcausally on the classical world, as well as to modify the ongoingbehavior of the single or coupled Trans-Turing systems. Finally, localalterations can alter which quantum degrees of freedom are entangled,thereby altering: i. which now classical degrees of freedom arecorrelated upon their quantum measurement; ii. if qualia are associatedwith quantum measurement, entangled quantum degrees of freedom may yielda unity of conscousness, that is, a solution to the qualia bindingproblem. Shifting patterns of entanglement in effect, shift the “focusof attention” of the coupled Trans-Turing systems.

A further feature of note in considering either neural systems withsynapses, or more general networks of Trans Turing systems arises asfollows. Consider a classical physics volume with a classical physicsgas in it. Does measuring the position and momentum of one classicalparticle give any insight into the SHAPE of the volume, or “box”? No. Bycontrast, a quantum wave behavior in a classical potential well thatserves as its BOUNDARY CONDITIONS, “feels” or “knows” its boundaryconditions which show up, for example, and without limitation, in thespectrum of its energy levels. Thus the wave property of a quantumsystem knows the SHAPE of its boundary condition potential well.

Consider by analogy, a room filled with music. Now consider breaking theroom into tiny 3 dimensional volumes and measuring pressure in each as afunction of time, then analyzing these via a digital “propositional”computer. Compare this to an analogue in which 1000 differently shapeddrum heads are placed around the music filled room. The spectral(eigenfunction) patterns of vibration of the diverse drum heads, eachreflecting the boundary conditions arising due to the shape of its drumhead, “know” in a non-propositional and analogue way the music in theroom. Telephones used to work in this way.

Similarly, consider the tens of billions of synapses in the brain, wheresensory inputs from the world, and classical physics firing of actionpotentials, TUNE the tiny time/space synaptic and local dendritictransmembrane potentials that serve as part of the potential well, orboundary condition on possible coherent or Poised Realm quantum wavebehaviors among, say, neurotransmitter receptor molecules. Then theenergy levels and other behaviors of those molecules, or any otherrelevant quantum or Poised Realm molecules or components, “Know”, theshapes of their potential well boundary conditions. But this means thatproper tuning of those boundary conditions allow the Poised Realm, henceprobably Trans-Turing behaviors, in the synapsic region to know theirexternal world. By entanglement of quantum degrees of freedom, coherentor Poised Realm, in properly tuned sets of potential wells, and quantummeasurement of many entangled quantum degrees of freedom, tuned andhighly correlated qualia are achieved, so a unity of consciousness isachieved, solving the neural binding problem. Thus, neural devices madeas above may achieve this.

More generally, the same holds for a plurality of Trans-Turing systemswhose potential wells are constituted in part by classical degrees offreedom, and which can be tuned, like the drum heads, to reflect in acoordinated way the “world” around the set of Trans-Turing systems. Theycollectively “Know” their embedding world, and do so in anon-propositional way. In turn, the lack of a propositional form, allowssuch evolving Trans Turing systems, see just below, to solve the Frameproblem of computer science via Darwinian preadaptations and othermeans.

Evolving Trans-Turing Systems for Desired Behaviors.

Trans Turing systems can be studied either by simulation or byconstruction of embodied trans-turing systems. In either case, to“program” a trans-turing system to achieve a desired behavior, apreferred means is to use some analogue of the Holland GeneticAlgorithm, or more generally an adaptive strategy using generations ofpopulations of variant Trans-Turing systems, choosing the “best” subsetof the members of each generation, keeping these unmodified and slightlymodified to create a next generation of Trans-Turing systems, andselecting the fittest by some “figure of merit” or selection criterion.

In general, any combination of time constant or time varying classical,poised realm, and quantum coherent inputs and outputs can be used todefine a figure of merit. As a non-limiting example, generalized“pattern recognition” on a set of quantum coherent, eg laser, poisedrealm, eg from another Trans-turing system, and classical inputs can beused as inputs, and output behavior that classifies these intoalternative time constant or time varying patterns of quantum coherent,poised realm, and classical outputs can be the figure of merit that isthe basis of selection on successive generations.

In general, any such mapping of inputs to desired outputs, classed inany way by the Trans-Turing system, creates a “fitness landscape” overthe space of parameters used to vary the structure and coupling amongthe variables in the Trans-Turing system or set of interactingTrans-Turing Systems. It is well known in the art that the statisticalfeatures of this fitness landscape for any single figure of merit may besimple and single peaked, or “rugged” and multipeaked, and even “random”with many local peaks. It is known in the art that recombination worksas an adaptive strategy on landscapes which are not too rugged(Kauffman, Origins of Order, Oxford Univ Press 1993 incorporated here byreference, (11)).

More generally, if there are multiple figures of merit and theirrelative importance is not definable, Global Pareto optimality is, asknown in the art, the sensible solution concept.

It will be clear to those of ordinary skill in the art, that TransTuringsystem may be embodied in self reproducing “protocells” able toreproduce, and yield heritable variations, thus undergo adaptiveevolution given a figure of merit, and undergo Darwinian preadaptations,also called Exaptations, (see Kauffman Investigations, Oxford UniversityPress 2000, and Reinventing the Sacred, Basic Books, 2008 bothincorporated here by reference, (12,13). Critically, exaptations allowNEW functions to emerge. As a concrete example, some fish have swimbladders, sacs filled with air and water, whose ratio determines neutralbuoyancy in the water column. These evolved by preadaptations from thelungs of lung fish. Here a new function, neutral buoyancy, arose in thebiosphere. This new function SOLVES the “FRAME PROBLEM” in computerscience. The frame problem consists in the following: picture a robotwith a standard digital computer on board. Many features of the robotand, say room it is in, are described FINITELY and given “affordances”.Here, for example the arm of the robot has a finite number of describedfeatures, each with FINITE LIST of propositionally defined affordances:Is a, Does A, Needs A, . . . The frame problem is this: Given a task, weare NOT guaranteed that the robot can deduce from the finite listpropositionally defined affordances the solution to the task.

But preadaptations of Trans-Turing systems that are evolving orco-evolving, as in the case of the evolution by preadaptation swimbladders which confer neutral buoyancy in the water column by the ratioof air and water in the swim bladder, evolved from the lungs of lungfish, yield the novel function of the swim bladder: neutral buoyancy.This new function, in general, would never be represented a finite listof affordances propositionally concerning the lungs of lung fish.Preadaptations arise in evolving embodied systems that are Kantianwholes in which the whole where the part exist for and by means of thewhole, and the whole exists for and by means of the parts. As anon-limiting example, collectively autocatalytic sets of polymers suchas peptides, (14), are such Kantian wholes. Gonen Ashkenazi, (15), atBen Gurion University in Beer Sheeba Israel has a nine peptidecollectively autocatalytic set. Here no peptide catalyzes its ownformation, but the formation of another peptide from smaller peptidesthat are “food” fed to the system, and are fragments of the “other”peptide in question. It is essential that in the collectivelyautocatlalytic set, no peptide catalyzes its own formation. Callingcatalysis of a specific reaction a catalytic “task”, the nine peptidesystem achieves CATALYTIC TASK “CLOSURE (11,14). All the reactions thatmust be catalyzed ARE catalyzed by some peptide in the collectivelyautocatalytic whole.

A collectively autocatalytic peptide system is an example of a Kantianwhole. The parts exist in the universe by means of the whole, and thewhole exists in the universe by means of the parts (16).

Now consider an evolving cell. It too achieves a closure in a set oftasks. But these are far wider than catalysis, and include makingmembranes, vectoring proteins to specific organelles in the cell, doingwork cycles, and reproducing by mitosis.

The next essential point to realize about the evolution of Kantianwholes is that each part has consequences. For a Trans-Turing systemthese are quantum coherent, poised realm, and classical. But there is noorderable or finite list of the consequences of any part alone or withindefinitely many other parts. Further, for each consequence there is noorderable or finite list of potential USES of that consequence. Yet, forthe ongoing evolution of the Kantian whole, by heritable variations andsome form of selection, all that is needed is that at least ONE, or aplurality of consequences of one or a plurality of parts, FIND SOME USEamong their consequences that enhances the fitness of the KantianTrans-Turing whole with respect to any figure of merit. This allows, viaquantum and/or poised realm/ and or classical consequences, newfunctionalities to emerge that are not logically entailed by a finitelist of propositional statements of affordances of parts of, eg a robotor standard computer. The embodied Trans-Turing system solves the frameproblem, never solved in computer science.

In one preferred embodiment of this invention, Trans-Turing systems arepart of evolving and convolving protocells with an autocatalytic set ofpolymers, RNA or proteins or any other polymers, or merely anautocatalytic set of molecules, housed in a reproducing liposome. Hereliposome reproduction has been achieved experimentally, (17).Collectively autocatalytic sets have been achieved experimentally.Recent work shows that such sets can undergo open ended evolution, (18),and if contained in a liposome that undergoes growth and budding, theautocatalytic set can typically synchronize its own reproduction withthat of the liposome. (19). In short, Trans-Turing systems capable ofevolving and co-evolving in protocells are now feasible and can evolveto adapt to a known figure of merit by adaptations or preadaptations,where the both solve the computer science Frame Problem.

Craig Ventner has recently created an “artificial cell” with DNA, RNAand encoded proteins, able to reproduce and create desired proteins,(20). It will be clear to those of ordinary skill in the art that suchsystems can be used to create populations of evolving Trans-turingsystems, using encoded proteins and a metabolism of smaller organicmolecules capable of Poised Realm and Trans-Turing behavior. Thepositions of these molecules on the X axis can be calculated using ourgraph theoretical procedures, and experimentally verified using powerlaw versus exponential decoherence rates.

More, the artificial cell can embody a genetic regulatory net oftranscription factors which activate and inhibit one another. Thisnetwork, (see Kauffman, 1993, Origins of Order), can be dynamicallyordered, critical or chaotic. The most controllable behavior occurs forcritical networks. There is evidence that real cells are critical,(Nykter et al, (21). This classical critical behavior can be married toTrans-Turing behavior which is also critical, to achieve Trans-Turingsystems that optimize the diversity of organized behaviors of the totalsystem. Here the degree of organization of a causal process can bemeasured by its power efficiency per unit fuel, and the choice of whichcausal process to consider among a set of interwoven causal processes ofeach part of the system can be chosen to maximize Set Complexity,defined elsewhere in this patent application. This can be generalized tomeasure set complexity of the total quantum and classical aspects of thesystem, as specified in this patent application elsewhere.

In another embodiment of Trans-Turing systems, these can be constructedusing nano-tube structures of arbitrary sizes and two or threedimensional structure, with chlorophyll and antenna proteins, or anyother atoms of molecules, affixed at known or variable positions on thenanotube structure, and capable of quantum coherent, open quantum PoisedRealm, and classical behaviors, to create one or any population ofTrans-Turing systems. By fabrication or any other means, know or in thefuture known, a population of similar or increasingly diverse TransTuring systems can be constructed, and in parallel with the discussionabove, can be selected by evolution, or co-evolution of interactingidentical or diverse Trans Turing systems, to increasing fitness withrespect to single figures of merit, or, using global pareto optimality,for optimal solutions to a set of figures of merit where the relativeimportance of the plurality of success criteria are not specifiable.

REFERENCES

All of which are incorporated herein by reference in their entirety.

-   1. Frankenberg, N., Hager-Braun, C., Teiler, U. Fuhrmann, M., Rogl,    H., Schneebauer, N., Nelson, N., and Hauska, G. (2008).    P840-Reaction Centers from Chlorobium tepidum-Quinone Analysis and    Functional Reconstitution into Lipid Vesicles. Photochemistry and    Photobiology, 64:(1), 1-14.-   2. Jones, M. R., McEwan, A. G., and jackson, J. B. (2010). The role    of c-type cytochromes in the photosynthetic electron transport    pathway of Rhodobacter capsulatus. Biochimica et Biophysica    Acta-Bioenergetics, Vol 1019, issue 1, 59-66.-   3. Gabellini, N. Gao, Z., Oesterhelt, D., Venturolli, G., and    Melandri, B. A. (1989). Reconstitution of cyclic electron transport    and photophosphosphorylation by incorporation of the reaction    center, bc1 complex and ATP synthase from Rhodobacter capsulatus    into ubiquinone-10/phospholipid vesicles. Biochimica et Biophsica    Acta-Bioenergetics, Vol 974, issue 2: 202-210.-   4. Varga, A. R., and Staehelin, L. A. (1985). Pigment-Protein    Complexes from Rhodopsuedomas palustris: Isolation,    Characterization, and Reconstitution into Liposomes. Journal of    Bactriology, vol 161 no 3: P 921-927.-   5. Scholes, G. D., (2010). Quantum-Coherent Energy Transfer: Did    Nature Think Of It First? The Journal of Physical Chemistry Letters,    1: 2-8.-   6. Pascher, T., Polyutov, S. Yartsev, A., Pullerits, T.,    Lenngren, N. (2011), Photon echo spectroscopy, Wikipedia.-   7. Hahn, E. L. (1950). “Spin Echoes”. Phys. Rev. 80: 580-594.-   8. Mezel, F. (ed) (1980) Neutron Spin Echo, Lecture Notes in    Physics, vol 128, Springer-   9. Science News Nov. 20, 2010. Inducing Entanglement.-   10. Francis Crick, The Astonishing Hypothesis: The Scientific Search    For the Soul, TOUCHSTONE, Simon an Schuster, N.Y. 1994.-   11. Kauffman, S. A. Origins of Order, Oxford University Press, N.Y.    (1993).-   12. Kauffman, S. A. Investigations, Oxford University Press, N.Y.    (2000).-   13. Kauffman, S. A. Reinventing the Sacred. Basic Books, N.Y.    (2008).-   14. Kauffman S. A. (1986). Autocatalytic Sets of Proteins. J. Theor.    Bio. 119: 1-24.-   15. N. Wagner and Ashkenasy, G. (2009). Symmetry and order in    systems chemistry. The Journal of Chemical Physics, 130:    164907-164911.-   16. Kauffman, S. A. Origins of Order, Oxford University Press. N.Y.    (1993).-   17. P. L Luisi, Stano, P., Rasi, S., and Mavelli, F. (2004). A    possible route to prebiotic vesicle reproduction, Artificial Life,    10: 297-308.-   18. C. Fernando, Vas as, V., Santos, M., Kauffman, S., and    Szathmary, E. (2011). Spontaneous Formation and Evolution of    Autocatalytic Sets within Compartments. Submitted.-   19. A. Filsetti, Serra, R., Carletti, T., Villiani, M., and    Poli., I. (2010). Non-linear protocell models: synchronization and    chaos. Eur. J. Phys. J. B 77: 249-256.-   20. R. L. Hotz. (2010). Scientists Create Synthetic Organism. Wall    Street Journal May 21.-   21. Nykter, M., Price, N. D., Aldana, M., Ramsey, S. A.,    Kauffman, S. A., Hood, L., Yli-Harja, O. and Shmulevich, I. (2008).    Gene Expression Dynamics in the Macrophage Exhibit Criticality. Proc    Natl Acad Sci USA 105(6): 1897-1900.

Unless otherwise indicated, all references disclosed herein areincorporated herein by reference in their entirety.

What is claimed is:
 1. A method of drug discovery, comprising: selectinga biological target; screening a library of candidate molecules byconducting an in vitro binding assay to identify a first subset ofcandidate molecules that bind to the biological target; determining theenergy level spacing distribution of a quantum degree of freedom in eachof the candidate molecules in the first subset by evaluating their meanenergy level spacing as a function of energy; comparing the energy levelspacing distribution to at least one pre-determined reference functionto determine a degree of similarity of the energy level spacingdistribution and the reference function; and selecting a second subsetof molecules from the first subset as drug candidates for drugdevelopment or medicinal chemistry based on the comparison, wherein thesecond subset of molecules are more likely to contain biologicallyactive molecules than the first subset of molecules.
 2. The method ofclaim 1, wherein the biological target is an enzyme.
 3. The method ofclaim 1, wherein the biological target is a receptor.
 4. The method ofclaim 3, wherein the receptor is a cell-surface receptor.
 5. The methodof claim 1, wherein determining the energy level spacing distributioncomprises spectroscopically determining the energy level spacings ofeach candidate molecule in the first subset.
 6. The method of claim 5,wherein the energy level spacings are determined usingultraviolet/visible spectroscopy.
 7. The method of claim 5, wherein theenergy level spacings are determined using infrared spectroscopy.
 8. Themethod of claim 5, wherein the energy level spacings are determinedusing X-ray spectroscopy.
 9. The method of claim 5, wherein the energylevel spacings are determined using nuclear magnetic resonancespectroscopy.
 10. The method of claim 5, wherein the energy levelspacings are determined using electron paramagnetic resonancespectroscopy.
 11. The method of claim 1, wherein determining the energylevel spacing distribution comprises computationally modeling the energylevels.
 12. The method of claim 1, wherein the one or more referencefunctions include a function having the form:p(s)=4sexp(−2s) where s is the energy level spacing and p(s) is theenergy level spacing distribution.
 13. The method of claim 1, whereinthe one or more reference functions include a function having the form:${p(s)} = {\frac{\pi \; s}{2}{\exp \left( {{- \pi}\; s^{2}\text{/}4} \right)}}$where s is the energy level spacing and p(s) is the energy level spacingdistribution.
 14. The method of claim 1, wherein the one or morereference functions include a function having the form:p(s)=exp(−s) where s is the energy level spacing and p(s) is the energylevel spacing distribution.
 15. The method of claim 1, wherein comparingthe energy level spacing distribution to at least one pre-determinedreference function comprises determining the quantity:${x = {{\frac{A - A_{p}}{A_{w} - A_{p}}\mspace{14mu} {wherein}\mspace{14mu} A_{p}} = {\int\limits_{2}^{\infty}{p_{p}(s)}}}},{A_{w} = {\int\limits_{2}^{\infty}{p_{w}(s)}}},{and}$${{A = {\int\limits_{2}^{\infty}{p(s)}}},{{{where}\text{:}\mspace{14mu} {p_{p}(s)}} = {{\exp \left( {- s} \right)}\mspace{14mu} {and}}}}\;$${{p_{w}(s)} = {\frac{\pi \; s}{2}{\exp \left( {{- \pi}\; s^{2}\text{/}4} \right)}}},$wherein s is energy level spacing and p(s) is the determined energylevel spacing distribution.
 16. The method of claim 15, whereinselecting a second subset of molecules from the first subset as drugcandidates comprises selecting those molecules having an x value withina predetermined distance from a predetermined value.
 17. The method ofclaim 1, wherein comparing the energy level spacing distribution to atleast one pre-determined reference function comprises fitting thedetermined energy level spacing distributions to a pre-determinedfunction.
 18. The method of claim 17, wherein selecting a second subsetof molecules from the first subset as drug candidates comprisesselecting those molecules whose energy level spacing distribution fitsthe pre-determined function.
 19. The method of claim 1, furthercomprising conducting an in vitro or in vivo assay on each drugcandidate to test for biological activity.
 20. A method of drugdiscovery, comprising: selecting a biological target; screening alibrary of candidate molecules by conducting an in vitro binding assayto identify a first subset of candidate molecules that bind to thebiological target; determining the energy level spacing distribution ofa quantum degree of freedom in each of the candidate molecules in thefirst subset by evaluating their mean energy level spacing as a functionof energy; conducting an in vitro or in vivo assay for biologicalactivity on each of the candidate molecules in the first subset;correlating the energy level spacing distribution with activitydetermined from the in vitro or in vivo assay; determining the energylevel spacing distributions of a quantum degree of freedom in a new setof candidate molecules by evaluating their mean energy level spacing asa function of energy; comparing the energy level spacing distributionsof the new set of candidate molecules with energy level spacingdistributions that correlate with biological activity to determine theirdegree of similarity; and selecting as drug candidates from the new setof candidate molecules for drug development or medicinal chemistry thosemolecules whose energy level spacing distributions exhibit apre-determined level of similarity to the energy level spacingdistributions that correlate with biological activity, wherein theselected drug candidates are more likely to contain biologically activemolecules than non-selected molecules from the new set of candidatemolecules.
 21. The method of claim 20, wherein comparing the energylevel spacing distributions of the new set of candidate molecules withenergy level spacing distributions that correlate with biologicalactivity comprises using a computational fitting algorithm.
 22. Themethod of claim 21, where the fitting algorithm comprises least squaresanalysis.
 23. A method of drug discovery, comprising: selecting abiological target; screening a library of candidate molecules byconducting an in vitro binding assay to identify a first subset ofcandidate molecules that bind to the biological target; measuringdecoherence decay of a quantum degree of freedom in each of thecandidate molecules in the first subset; comparing the decoherence decayto at least one pre-determined reference function to determine a degreeof similarity of the decoherence decay and the reference function; andselecting a second subset of molecules from the first subset as drugcandidates for drug development or medicinal chemistry based on thecomparison, wherein the second subset of molecules are more likely tocontain biologically active molecules than the first subset ofmolecules.
 24. The method of claim 23, wherein the reference functionhas the form:S(T _(H))˜exp(−T _(H) /T _(D))/T _(H) ^(α) wherein S(T_(H)) is acoherence signal as a function of time T_(H) and T_(D) and α are fittingparameters.
 25. The method of claim 24, wherein selecting the secondsubset of molecules comprises selecting those molecules having thelowest T_(D) value.
 26. The method of claim 23, wherein measuringdecoherence decay comprises performing a spin echo experiment.
 27. Themethod of claim 23, wherein measuring decoherence decay comprisesperforming a photon echo experiment.
 28. A method of drug discovery,comprising: selecting a biological target; screening a library ofcandidate molecules by conducting an in vitro binding assay to identifya first subset of candidate molecules that bind to the biologicaltarget; measuring decoherence decay of a quantum degree of freedom ineach of the candidate molecules in the first subset; conducting an invitro or in vivo assay for biological activity on each of the candidatemolecules in the first subset; correlating the decoherence decay withactivity determined from the in vitro or in vivo assay; measuringdecoherence decay of a quantum degree of freedom in a new set ofcandidate molecules; comparing the decoherence decay of the new set ofcandidate molecules with the decoherence decay that correlate withbiological activity to determine a degree of similarity of thedecoherence decay of the new set of candidate molecules and thedecoherence decay that correlate with biological activity; and selectingas drug candidates from the new set of candidate molecules for drugdevelopment or medicinal chemistry those molecules whose decoherencedecay exhibit a pre-determined level of similarity to the decoherencedecay that correlate with biological activity, wherein the selected drugcandidates are more likely to contain biologically active molecules thannon-selected molecules from the new set of candidate molecules.